Laws for legal moped usage vary by state in America. You may be able to find information on your state's transportation website but the following are likely to be more useful as some states make it hard to find moped related information
The term "motor-driven cycle" shall include every motorcycle weighing when fully equipped less than 200 pounds and every bicycle with motor attached and every motor scooter.
Licensing and Registration
- Section 32-12-22 - Registration; operator's license generally.
Every person,except a person holding a driver's license issued under authority of Chapter 6 of this title, before operating any motor-driven cycle upon a public highway in this state, shall register it with the Director of Public Safety and procure an operator's license. Operators' licenses shall be issued under and be governed by the provisions of Chapter 6 of this title; except, that such a license shall be issued to any person 14 years of age and older if such a person can satisfy the Director of Public Safety or an examining officer that he is competent to operate a motor-driven cycle with safety to persons and to property.
If you have a valid driver's license, registration is not necessary.
Any vehicle with pedals to permit propulsion by human power, having a seat or saddle for the use of the rider and designed to travel on not more than three wheels, with a motor rated not in excess of 2 brake horsepower and not capable of propelling the vehicle at a speed greater than 30 miles per hour on level ground, and with a power-drive system that functions directly or automatically without clutching or shifting gears by the operator after the drive system is engaged. If an internal combustion engine is used, the displacement may not exceed 50 cubic centimeters.
Licensing and Registration
- Registration is REQUIRED, NO title is required. This vehicle can be operated on the roadways of this state.
- Can not have electric start.
Taken from the Florida Department of Highway Safety and Motor Vehicles website. 
Rules and Regulations
Any person operating a moped upon a roadway at less than the normal speed of traffic at the time and place and under the conditions then existing shall ride as close as practicable to the right-hand curb or edge of the roadway except under any of the following situations:
- When overtaking or passing another vehicle proceeding in the same direction.
- When preparing for a left-turn at an intersection or into a private road or driveway.
- When reasonably necessary to avoid any condition, including, but not limited to, a fixed or moving object, parked or moving vehicle, bicycle, pedestrian, animal, surface hazard, or substandard-width lane, that makes it unsafe to continue along the right hand curb or edge. For purposes of this paragraph, a "substandard-width lane" is a lane that is too narrow for a moped and another vehicle to travel safely side by side within the lane.
- Any person operating a moped upon a one-way highway with two or more marked traffic lanes may ride as near the left-hand curb or edge of such roadway as practicable.
- A person propelling a moped solely by human power upon and along a sidewalk, or across a roadway upon and along a crosswalk, has all the rights and duties applicable to a pedestrian under the same circumstances, except that such person shall yield the right-of-way to any pedestrian and shall give an audible signal before overtaking and passing a pedestrian.
- No person shall propel a moped upon and along a sidewalk while the motor is operating.
- A violation of this section is a non-criminal traffic infraction, punishable as a moving violation as provided in chapter 318.
On Bike Lanes:
- Any road, path, or way that is open to bicycle travel, which road, path, or way is physically separated from motorized vehicular traffic by an open space or by a barrier and is located either within the highway right-of-way or within an independent right-of-way.
- No person shall drive any vehicle other than by human power upon a bicycle path, sidewalk, or sidewalk area, except upon a permanent or duly authorized temporary driveway. A violation of this section is a non-criminal traffic infraction, punishable as a moving violation as provided in chapter 318.
Moped is vehicle, Wood vs. State 
A moped is defined as any motor driven cycle with an engine not exceeding 50 cubic centimeters (3.05 cubic inches).
Licensing and Registration
- Rider must be 15 years of age and have in their possession a valid driver's license, instructional permit or limited permit.
- Mopeds are exempt from the provisions relating to the registration and licensing of motor vehicles.
- No tag is required.
- A Class M license is required to operate, legally, a motorcycle or motor-driven cycle in Georgia. Every motor vehicle having a saddle for the use of the rider and designed to travel on not more than three wheels in contact with the ground, but excluding a tractor and moped (with engine size less than 50CC), are defined as motorcycles. Georgia law places all types of motorcycles including scooters, motorbikes and minibikes (with engine size 51 CC or greater) into one classification. All are considered motor-driven cycles.
Rules and Regulations
Rules to operate mopeds on Georgia roads and highways:
- Must wear protective headgear (motorcycle helmet).
- Every person operating a moped upon a roadway must obey the same traffic laws governing drivers of motor vehicles.
- May not use limited access highways or other roadways where the minimum speed limit is above 35 mph.
Taken from Georgia Department of Driver Services
"Moped" means either a motorized bicycle:
- whose frame design may include one (1) or more horizontal crossbars supporting a fuel tank so long as it also has pedals, or a motorized bicycle with a step-through type frame which may or may not have pedals
- that is rated no more than two (2) brake horsepower
- has a cylinder capacity not exceeding fifty (50) cubic centimeters,
- has an automatic transmission not requiring clutching or shifting by the operator after the drive system is engaged
- and capable of a maximum speed of not more than thirty (30) miles per hour.
A moped is a bicycle that meets the following requirements:
- Is designed to be propelled by human power with some assistance from a motor.
- Has pedals that drive the bicycle mechanically
- Has two or three wheels, of which are more than 14 inches in diameter
- Has a motor with a rating of 1.5 brake horsepower or less, and, if the motor is an internal combustion engine, a capacity of 50 cubic centimeters piston displacement or less.
Motor Scooter Definition
A motor scooter is a type of non-pedaled vehicle that meets the following standards:
- Has two wheels, of which one is 10 inches or more in diameter
- Has a seat for the operator
- Has a step-through chassis
- Is equipped with an automatic transmission.
- Has a motor with a rating of 2.7 brake horsepower or less, and if the motor is an internal combustion engine, with a capacity of 50 cubic centimeters piston displacement or less.
Generally, motor scooters can achieve a speed of up to 40 MPH, but this varies by the manufacturer and model that you have. However, a motor scooter is not allowed to exceed the speed of 30 MPH on public roadways. There is no mention of maximum speed of mopeds, as they do not fall under the definition of motor scooters.
A scooter is a two-wheeled vehicle that has handlebars and is designed to be stood on by the operator. These devices cannot be legally operated on public roadways or sidewalks.
Moped Licensing and Registration
- To operate a moped in Maryland, riders must have a valid drivers license from which ever state that they live in, or a valid Maryland moped operator's permit issued by the Maryland MVA. Failure to present the proper licenses needed will result in a fine of around $315.
- All "motor vehicles" are required to be registered in Maryland, but vehicles classified as either motor scooters or mopeds are exempt from this law. So all mopeds and motor scooters do not need to be registered with tags in Maryland.
Moped Traffic Laws
- Moped operators are not required to wear a helmet.
- Mopeds cannot be operated on highways that have a speed limit greater than 50mph.
- Where there is a bike lane paved to a smooth surface or a shoulder paved to a smooth surface, a person operating a bicycle or a motor scooter shall use the bike lane or shoulder and may not ride on the roadway, except for common traffic procedures, which include:
- overtaking and passing another bicycle, motor scooter, pedestrian, or other vehicle within the bike lane or shoulder if the overtaking and passing cannot be done safely within the bike lane or shoulder
- preparing for a left turn at an intersection or into an alley, private road, or driveway
- When reasonably necessary to leave the bike lane or shoulder to avoid debris or other hazardous condition
- When reasonably necessary to leave the bike lane or shoulder because the bike lane or shoulder is overlaid with a right turn lane, merge lane, or other marking that breaks the continuity of the bike lane or shoulder.
- Gas and electric motorized toy scooters cannot be operated on sidewalks
- A person may not operate a bicycle or a motor scooter on any highway or roadway while the person is wearing any headset covering both ears
- For a printable version of Maryland moped traffic laws, download this pdf document.
Maryland Helmet Law Changes
In the 2006 legislative session in Maryland, House Bill 496 (PDF) brings up the debate about whether helmets should be required for the riders and operators of mopeds and motor scooters. The bill introduces the idea of making moped and motor scooter operators required to wear helmet and eye protection, just like the motorcycle laws. The law suggests riders under the age of 21 be required to abide by this law. Riders and operators over 21 would not be required to wear a helmet or eye protection if they can provide proof of proper medical insurance.
New Laws for 2012
Title, registration and tag required. Insurance will be required july 2016. A Helmet must be worn.
- Has no external shifter.
- Does not exceed 30 mph on flat ground.
- Has an engine less than 50cc.
In Oklahoma, mopeds and scooter are subject to all laws applicable to Motorcycles in regards to registration. The vehicle must be titled, tagged, and insured.
- No motorcycle license is required for a vehicle under 50cc that does not exceed 30 mph on flat ground.
- Helmets are required for riders under the age of 18.
In South Carolina, a moped:
- must have operable pedals
- be 50cc or less
- cannot exceed 1.5 brake horsepower
- cannot exceed 25mph
- must have an automatic transmission
"Moped" means every cycle with pedals to permit propulsion by human power and with a motor of not more than fifty cubic centimeters which produces not to exceed one and one-half brake horsepower and which is not capable of propelling the vehicle at a speed in excess of twenty-five miles per hour on level ground. If an internal combustion engine is used, the moped must have a power drive system that functions directly or automatically without clutching or shifting by the operator after the drive system is engaged. (Section 56-3-20)
Moped Licensing and Registration
Section 56-3-110 (Vehicles required to be registered and licensed) states that: "Every motor vehicle, trailer, semitrailer, pole trailer and special mobile equipment vehicle driven, operated or moved upon a highway in this State shall be registered and licensed in accordance with the provisions of this chapter. It shall be a misdemeanor for any person to drive, operate or move upon a highway or for the owner knowingly to permit to be driven, operated or moved upon a highway any such vehicle which is not registered and licensed and the required fee paid as provided for in this chapter."
However, a "motor vehicle" is defined as: "every vehicle which is self- propelled, except mopeds, and every vehicle which is propelled by electric power obtained from overhead trolley wires, but not operated upon rails." (56-3-20)
This would appear to exempt mopeds from the registration and licensing process.
Somewhere in the Motor Vehicle Financial Responsibility Act (Title 56, Chapter 9) and/or the Automobile Insurance chapter (Title 38, Chapter 77), it probably says that all motor vehicles are required to carry some form of liability insurance. However, for the purposes of chapter 9, a motor vehicle is defined as: "every self-propelled vehicle which is designed for use upon a highway, including trailers and semitrailers designed for use with such vehicles but excepting traction engines, road rollers, farm tractors, tractor cranes, power shovels, mopeds, and well drillers, and every vehicle which is propelled by electric power obtained from overhead wires but not operated upon rails;"
This would appear to exempt mopeds from insurance requirements, although you should dig through the laws yourself and see if you can verify that information.
Rules and Regulations
- A driver's license is required to operate a moped. (56-1-1720)
- A moped must have a rear-view mirror, operable running lights, and a brake light which is operable when either brake lever is used (56-5-3720)
- All running lights must be on while the moped is being operated (56-5-3730)
- Between dusk and dawn, a headlight emitting white light visible 500 feet forwards and a tail light emitting red light visible 500 feet to the rear must be turned on (56-5-4450 and 56-5-4650)
Please search the South Carolina Code of Laws for full text of laws cited in this section.
Special Municipality Notes
The City of Charleston requires both registration and insurance for mopeds. 
- "Motorized bicycle" means a vehicle with two (2) or three (3) wheels, an automatic transmission, and a motor with a cylinder capacity not exceeding fifty cubic centimeters (50cc) which produces no more than two (2) brake horsepower and is capable of propelling the vehicle at a maximum design speed of no more than thirty miles per hour (30 mph) on level ground. The operator of a motorized bicycle must be in possession of a valid operator's or chauffeur's license, and shall be subject to all applicable and practical rules of the road. A motorized bicycle may not be operated on a highway of the interstate and defense highway system, any similar limited access multilane divided highway, or upon sidewalks;
- "Motor-driven cycle" means every motorcycle, including every motor scooter, with a motor which produces not to exceed five (5) brake horsepower, or with a motor with a cylinder capacity not exceeding one hundred twenty-five cubic centimeters (125cc);
- The driver of a motorcycle, motorized bicycle, as defined in chapter 8 of this title, or motor-driven cycle, and any passenger on any of these, shall be required to wear either a crash helmet meeting federal standards contained in 49 CFR 571.218
- Every motorcycle or motor-driven cycle operated upon any highway or public road of this state shall be equipped with a windshield, or, in the alternative, the operator and any passenger on any such motorcycle or motor-driven cycle shall be required to wear safety goggles, face shields, or glasses containing impact resistant lenses.
- Every motor vehicle or motorized bicycle, as defined in chapter 8 of this title, and every trailer, semi-trailer, and pole trailer as defined by § 55-1-105, when driven or moved upon a highway, and every mobile home or house trailer when occupied shall be subject to the registration and certificate of title provisions of chapters 1-6 of this title, except:
(7) Motorized bicycles, except when voluntarily registered under the provisions of § 55-4-101
- The owner of a motorized bicycle may, subject to the approval of the commissioner, apply for registration and registration plates for such motorized bicycle. The commissioner shall by regulation provide for the manner in which such single applications are to be made and the conditions under which they may be allowed; however, this provision shall not be construed as granting the commissioner authority to issue such registration and plates on any basis other than as is required in this chapter. Each applicant for registration under this provision shall be charged the same registration taxes imposed on Class (A) motor vehicles by § 55-4-111.
STEPS TO GETTING LEGAL:
Mopeds in Texas must be titled, registered and insured. The operator must have a Class M license endorsement.
Titling is the tricky part. If buying a moped in Texas, buy one with a title. OR BUY A MOPED FROM A STATE THAT DOESN'T REQUIRE TITLES FOR MOPEDS. Depending on WHICH STATE YOU BOUGHT IT FROM, you may just need the old registration or a bill of sale.
Insure your bike: Most major insurance companies offer moped insurance for very low rates.
Inspection is next. Bring your bike, title and proof of insurance to an authorized inspection station. Make sure you have a place to put the inspection sticker already on your bike, such as a license plate holder with a tab for an inspection sticker on it. They will NOT just hand you the sticker, it has to go right on your bike or plate holder.
Then bring your title, proof of insurance, and inspection report to your county tax office to register your bike and get plates. You will have to pay sales tax and registration fees.
TEXAS MOPED INFO:
Vehicle definitions: http://www.txdps.state.tx.us/msb/documents/VDRchart.pdf
Definition of a moped: "Moped" means a motor-driven cycle that cannot attain a speed in one mile of more than 30 miles per hour and the engine of which: (A) cannot produce more than two-brake horsepower; and (B) if an internal combustion engine, has a piston displacement of 50 cubic centimeters or less and connects to a power drive system that does not require the operator to shift gears. TTC 541.201(8) Note: any 2 or 3-wheeled vehicle that does not meet this definition is automatically classified as a motorcycle.
Mopeds must also be on this approved list: http://www.txdps.state.tx.us/msb/documents/CurrentMopedList.pdf
Info on Texas Class M license endorsement: http://www.txdps.state.tx.us/DriverLicense/motorcycleLicense.htm
Info on Inspection: http://www.txdps.state.tx.us/rsd/vi/inspection/inspectionCriteria.aspx
Helmet law: http://www.txdps.state.tx.us/msb/helmet.htm
There is no horsepower (hp) limitation under current Virginia law, there is a CC (cylinder displacement) limit and a 35 mph speed limit, which will redefine your moped as a motorcycle if exceeded. No license of the operator , you must be 16 or older and have some form of goverment ID with name, address and DOB, picture is required. Registration and tags required . Use this form if you have no proof of ownership http://www.mopedarmy.com/forums/file.php/1/122871/VSA12moped_1dmv.pdf The state speed limit is 35 mph or as posted, whichever is lesser. No , taxes or insurance. If you are suspended with DUI you may NOT operate a moped.
"Moped" means every vehicle that travels on not more than three wheels in contact with the ground that has (i) a seat that is no less than 24 inches in height, measured from the middle of the seat perpendicular to the ground and (ii) a gasoline, electric, or hybrid motor that displaces less than 50 cubic centimeters. For purposes of Chapter 8 (§ 46.2-800 et seq.) of this title, a moped shall be a vehicle while operated on a highway.
Dealers can't sell over 2p or more than 35 mph, but you can own and operate greater than 2 hp and capable of over 35 mph. § 46.2-915. Stickers required on mopeds.
Any dealer who sells any moped at retail shall affix to any such moped, or verify that there is affixed thereto a permanent decal or sticker which states (i) that the operation of mopeds on highways and public vehicular areas by persons under the age of sixteen is prohibited by Virginia law, (ii) the maximum horsepower of the moped, and (iii) the maximum speed at which the moped may be ridden.
Any dealer who sells any such moped which does not have affixed thereto such a permanent decal or sticker or who sells a motorcycle with such a sticker or decal attached thereto indicating that its motor is rated at no more than two brake horsepower producing only ordinary speeds up to a maximum of 35 miles per hour shall be guilty of a Class 1 misdemeanor.DOT Helmets are required by the state
§ 46.2-915.2. Ordinances providing for certain safety equipment for mopeds; effect of violation; penalty.
The governing body of any county, city, or town may, by ordinance, provide that every person operating a moped, as defined in § 46.2-100, on a public street or highway shall wear a face shield, safety glasses, or goggles of a type approved by the Superintendent or have his moped equipped with safety glass or a windshield at all times while operating such vehicle, and operators and passengers thereon, if any, shall wear protective helmets of a type approved by the Superintendent. A violation of any such ordinance shall not constitute negligence, be considered in mitigation of damages of whatever nature, be admissible in evidence or be the subject of comment by counsel in any action for the recovery of damages arising out of the operation, ownership, or maintenance of a moped or motor vehicle, nor shall anything in this section change any existing law, rule, or procedure pertaining to any such civil action. Any person who knowingly violates any such ordinance shall be guilty of a traffic infraction and be subject to a fine of not more than fifty dollars.
More info op what can and can't be done while riding here http://leg1.state.va.us/000/lst/LS951608.HTM
From the DMV website:
Virginia Code section 46.2-100 defines a moped as a vehicle that:
* travels on three wheels or less, * a seat that is no less than 24 inches in height, measured from the ground to the middle of the seat, and * has a gasoline, electric, or hybrid motor that displaces less than 50 cubic centimeters.
Operation of mopeds on any Interstate Highway System is prohibited by Virginia Law. Operation of mopeds on highways and public vehicular areas by persons under age 16 is prohibited by Virginia law.
Moped riders must carry some form of identification that includes name, address, and date of birth.
Although you do not need a driver's license to operate a moped, you may not operate a moped if you have been declared a habitual offender or your license is suspended or revoked for driving under the influence of alcohol or drugs.
Moped drivers are required to abide by the same traffic laws and regulations as automobile drivers. Detailed information on Virginia's traffic laws and regulations is available in the Driver's Manual. In addition, certain local governments may impose restrictions on moped operation. Violations of the moped laws are considered a traffic infraction and convictions will appear on your driving record.
All DUI laws apply to mopeds operated on public highways.
No moped shall be driven on any highway or public vehicular area faster than 35 miles per hour. If you operate a moped faster than 35 miles per hour, Virginia law deems this to be operating a motorcycle, which requires you to title and register the moped as a motorcycle and obtain a motorcycle license. Operation of mopeds is prohibited on any Interstate Highway Component.
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|South||AL • FL • GA • KY • MD • NC • SC • TN • TX • VA|
|Midwest||Illinois • Iowa • Kansas • Michigan • Minnesota • Missouri • Ohio • South Dakota • Wisconsin|
|West||Arizona • California • Colorado • Hawai'i • Montana • Nevada • New Mexico • Oregon • Utah • Washington|