One DM I know has run two games (not campaigns) in which the assassin PC successfully offed all the other PCs. We "re-booted" one of the games because we wanted to finish the dungeon.
I ran a campaign (more than one game) with two Evil characters (four Neutral or Good) and somehow they all stayed working together. I'm not sure how (or whether) I managed that, but my suspicion is that it had something to do with the fact the characters had a vested interest in their mutual survival. The characters were certainly not Bright, Shining Heroes but were rather thrust (unceremoniously) into a situation where they basically had to deal with whatever I threw at them. (Plus, it was a college game, so very laid-back motivation-wise. This was where I learned the lesson "make the *players* worry, and their characters will follow suit.")
I'm inclined to agree with the above (various posters) that Evil characters are, for the most part, a result of "competitive" players. Players that don't want any time out of the spotlight; players that don't want (their characters) to behave the way someone else (the game milieu) tells them they ought to behave; players that think their Evil characters (and by extension, they themselves? Pop psych here) are "cooler" somehow; players that like the thought of "getting away" with stuff they could never do in real life.
I'd posit that, as in many DM vs. player "style" conflicts, the choice of an anti-heroic campaign versus a heroic campaign often leaves very little room for compromise. About the only wiggle room you get is to appeal to the Evil character's selfish nature and "prove" (through plot/adventure development) that going along with the Good characters is going to be the more attractive option *always* (as per green slime's example).
Cogito ergo uh-oh. I think, therefore something's about to go wrong.
[EDIT: Thanks, Keith. Your post reminded me of the plot acrobatics required to keep the Evil characters toeing the line. Also reminds me of Autolycus from "Hercules: The Legendary Journeys" (Bruce!!): while not particularly Evil, certainly a character who did good deeds (at least in his first few appearances) only because they were in his best interest. I should add that I usually simply prohibit Evil characters these days, because they're too much of a pain in the rear... but I'm also lucky enough to be in a group where it's not an issue.]