Well, I don't take the time to find out/come up with "names" of the oddballs wandering my streets, but I've seen my fair share of nuts. My brother says that he went to the library for school once and there was some raggedy-looking guy nearby making faces at the kids in his class. Also, there's some dude with... well, I think I've seen him once or twice from a distance, but I think he's got, like, Twin Virus-style white dreadlocks, though it might be just long, white hair.
I've had the unfortunate experience of coming across someone in public with Tourette's twice (once was in Strawberry fields in New York, which kind of ruined the moment). I can't say for sure if they were homeless, but I'd figure.