Local to RI although very slowly spreading to nearby MA:
1) Hot wieners. Bun, piece of wiener meat (Easy Boys!) which is NOT a hot dog but similar although kept in a steam chamber, covered with meat sauce (do not even ask what is in that), then covered in raw onions and a swipe of yellow mustered. Also called 'gaggers', 'belly- busters' and a whole host of cute names. An RI institution served in many New York System restaurants (which are NOT in New York). Commonly called 'Hot wennies' in RI speak 'cause we don't need no 'R's.
2) Coffee milk, coffee ice cream. Local company makes 'coffee syrup', sort of like chocolate syrup but thinner, stronger and made from the extract of coffee grounds. Very popular here.
3) Del's Lemonade. Which is not lemonade. It is a lemon and sugar and chipped ice concoction. Unique to RI as far as I know- sweeter and thicker than something like Italian Ice, for example. Spring COG rally 2011 served a bunch to the visiting COGgers and it went over quite well, or at least I think (hope?) it did. The stuff is unique because of the stainless steel drums it is made inside of, with long, curved scrapers rubbing the outside of the frozen drum. It is just not like anything that comes out of a blender, for example.
Brian
I suppose if this thread is to survive we may need to add regional specialties that are different from elsewhere just because they aren't available most places. Anybody here from Michigans's U.P. want to tell us about hot pasties? They sound like those tassel things that some strippers use, but they aren't.