The purpose of this article is to serve as a place to document the laws and behavior of various states in regards to operating a moped in one state which has been registered in another with different registration regulations.
All States
According to the Intermodal Surface Transportation Efficiency Act of 1991, describes a 'Single State Registration System' in which "such single State registration shall be deemed to satisfy the registration requirements of all other States.", therefore riding a moped registered in a state such as Massachusetts where a mere $40 sticker is necessary to comply is deemed satisfy the registration requirements of a state such as Rhode Island where normally one would be required to have insurance and plates.
See http://codes.lp.findlaw.com/uscode/49/IV/B/145/14504 or http://ntl.bts.gov/DOCS/istea.html
Update: this law appears to only apply to commercial cargo vehicles.
New York
On August 12, 2010 Dave Seley spoke with the New York Department of Motor Vehicles (DMV) supervisor 'Shirley' in the Albany District Office (1-518-473-5595). After much explanation on his part, she agreed with his argument that New York must honor Massachusetts registrations including mopeds. She advised him to fax the NYDMV legal department so they can fax him back something in writing to carry so as not to get ticketed by an officer who does not know the federal law regarding interstate registration reciprocity. She confirmed the requirements for mopeds in the Polk, the book the cops use. The initial fax by Dave may be seen here and their response may be seen here.
Rhode Island
31-3-2.1 states that "Out-of-state residents owning motorized bicycles, whose state of residence does not require the registration of those vehicles, shall register the vehicles in the state of Rhode Island and upon payment of the registration fee shall be issued stickers to be placed on the vehicle evidencing registration." It is not clear as to whether or not the state expects one to register in advance. If this were the case, it could be a violation of federal law.
I spoke with the RI DMV enforcement department on 03/30/2011 regarding this matter and was told that the issue is not the plate, but the insurance. In other words, if you can prove you are registered in Massachusetts or another plate-less state (carry the paperwork that came with your sticker) and can show that you are insured, the state of RI will be happy. I am in the process of contacting the representatives from the registration department to discuss how the 'full faith and credit' clause of the Constitution affects their laws.