Yes, at one time, back around 1900, it was expected that cyclists carry. I've seen old ads for cyclists' handguns. There are also archaic laws in the books that permit cyclists to dispatch animals that are a nuisance. Ah, for the good old days.
I've often thought that cyclists should be able to carry in order to level the playing field against the motorists out in traffic. But you'd have to have a pretty accessible holster in order to respond in time to motorist attacks. Probably a better solution, which technology is rapidly evolving into, would be tiny front and rear video cams that record an hour of images onto an SD card, tied in with the bike computer so that the cameras turn off about a minute after the bike comes to a stop, rubber side down or not. This way you'd have a record of how the motorist hit you whether or not you're still alive. Hell, I'd like to see this sort of thing black-boxed into cars and required for insurance or accident investigation purposes.
Anyway, what to carry? A Glock would be the most fool-proof and quick. One that shoots S&W .40 cal for the stopping power...
L.