In terms of head-to-head stuff (potentially OT):
Back in the day, we had a guy run a homebrew post-Apocalyptic RPG where half of us were "Good Guys" and half were "Bad Guys". He didn't even tell us this to start with...we couldn't figure out why it was taking so long for two halves of the party to meet..
On one hand, it was fun in a PvP adrenaline rush kind of way.
On the other hand, it really didn't work so well in the long run. There was a heavy down-time component - as anyone with a group that likes to split the party knows, this is a bear for the GM to manage, and hard to do well. Also, PCs are generally the wrecking crews of their particular Universes, and when two groups of them meet head-to-head, it gets pretty ugly.
My character ended up with a prosthetic jaw, and the guy who blew off his original set of chompers ended up disemboweled by my set of grapple-claws. Most of the rest of the PCs on either side fared worse...generally maimed or very, very dead...I don't even want to go into what was done to some of the corpses, but let's just say that, even by post-Apocalyptic standards of morality, lines were crossed.
And that was from one PvP encounter.
Had it been a standard table-top game, it would have worked, but as an RPG, people are just too into their characters, I think. GM's have to be able to act as a "neutral" judge in RPGs, but really...it's about the story, so at the end of the day, well-played PCs will reign triumphant. But if the PCs are fighting other PCs, then there's zero wiggle room for the GM to interpret the rules or rolls. Not a situation I'd want to be in, as GM...killing a PC is tough enough, but PC vs PC...ouch.
At least in my games, I've generally discouraged PvP...some sparring, here and there, and the occasional "heated discussion" that's been broken up before anyone needed a Raise Dead spell.
-Jn-
Ifriti Sophist