Now that some folks have shared theirs, I may as well share some of mine.
One character I've played in a zombie RP was this 20-something year old British lowlife. He was an alcoholic, made awkward passes at women, and liked to talk about his deviant sexual fantasies and party experiences. He was also next to useless against zombies, and one of the last posts I made with him involving him playing with himself instead of fighting off a horde of zombies like the rest of his team.
Another was this tall bearded 18 year old with the mentality of a socially inept 9-year old. He was the first character I ever RPed on the RP Guild back when I joined last year. He was incapable of functioning as a reliable member of the team, and he attempted to kill himself right before he got eaten alive by a pack of feral dogs.
The character in my avatar, who is pretty much my online persona and whose first name is my username here, is a character I've been thinking of RPing here. He'd definitely fit the bill for being a morally depraved character, but I haven't the courage to RP him here because of the more raunchy elements I've incorporated into his character.