In Living Greyhawk, I have seen some really good role-playing, for instance, one of the weasels of Pelor (what I call the clerics) tries to convert other player characters to Pelor throughout the game, in character, at taverns and so on. He won't ever get any experience for this (in a real campaign, I would give him some), but it makes his character seem more real.
I have also seen a bard played correctly, who tried to woo female characters (not always actually females IRL), and spent gold on them and flattered them, and vowed to protect them. It made the other players look flat. And nothing is odder than a man pretending to be flattered and trying to flirt back. Uh, on the other hand, maybe I don't want to think about that.
On the other hand, I have seen people play the dumbest things, for instance, one guy was in love with the warhorse he had bought, blah blah blah this and that about his horse all game long. It was then and there that I decided that my elf liked to eat horses, so I waited for my chance to cook it up...sadly, we had to go fight some bad guy before I could eat his horse...