I carry full strength pepper spray. It fits easily in a jersey pocket, and can be deployed quite accurately from the bike (effective range is about 12 feet). I use it about once every 6000 miles or so, on average. The pepper spray does not seem to hurt the dogs (they don't whimper or cry), but they immediately lose all interest in chasing me. I'll typically use it on dogs trying to overtake me from the rear. Even if I could outrun them, I'll give them a shot of pepper if my loud "No" doesn't make them stop. Most dogs are smart enough that after getting sprayed once, they won't chase me again.

The pepper spray also provides a bit of confidence in case of an encounter with a two-legged varmint, but I've never had to use it in those situations.