Mail in Registration
There is a forum post about this topic, but I felt the need to preserve this information in a more permanent location. 
This article is based off the original post by randycareagain and fizzleaid and my own successful experience using Vermont's Mail in Registration.
The main webpage and information can be found at http://dmv.vermont.gov/help#VehicleRegistration
You do NOT need to be a resident of Vermont to use this service.
Yes - That means you can register your moped in your own state through Vermont.
FIRST - You need to do is take 3 photos of your bike.
- A close up of the VIN plate
- A photo of the VIN plate on the bike
- A photo of the whole bike
SECOND - Fill out the VD-119 form, located here 
Here's the hard part -- fill out VD-119 as follows:
- Circle "Owned"
- Owner/Lessee: this is you (not the seller), use your address
- VT License: Put "SSN: ###-##-###" if out of state
- Name of person or company vehicle acquired from: seller/friend, who you bought or 'bought' this moped from
- Address of of person or company vehicle acquired from: seller/friend's address
- Signature of of person or company vehicle acquired from: seller/friend signature
- Circle "New Registration"
- Registration/Plate Type: in the write-in section, write "Motor driven cycle" in the left-hand space, and "17" in the right-hand space
- Make, Model, Year, Color, Mileage: all your bike's legit actual info
- Body Type: MDC
- Serial Number: VIN of the bike
- Cylinders: 1
- Circle "Used"
- Circle "Gas"
- Cycle/ATV: write "2" in # of wheels, and "49" in CCs
- Purchase price: write $500
- Net taxable: write $500
- Registration, on the right: write $30
- Tax: write $30
- Sign it!
THIRD - Fill our a VERMONT Bill of Sale located here  You only have to fill out the Bill of Sale portion, don't bother with the odometer page. Make sure you use the same info for the Bill of Sale as what is written in 5B on your VD-119
FORTH - Make a check out to "Vermont Department of Motor Vehicles" for $60 (As mentioned in 6A from step 2 the minimum taxable amount is $500…. $30 for registration and $30 tax on $500, totaling $60)
LAST - Put your 3 photos, VD-119, Vermont Bill of Sale, and check in an envelope and mail it to:
Vermont Department of Motor Vehicles
120 State Street
Montpelier, Vermont 05603
They won't deposit your check unless everything is okay.
If everything goes smoothly you should have your registration in ~2 weeks, and your plate in ~4 weeks.