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In a Wicked Age... comes to mind!
In A Wicked Age and Smallville are the only two I can think of that really embraced the PVP ethos completely.
For true PvP you'll want something like Paranoia, a game where the players are actually trying to undermine and conquer each other instead of just going through the motions for the sake of dramatic form.
I'll give special mention to the Finnish story game Tales of Entropy just because it's something I've been playing a lot lately myself, and because it's a very pure-bred example of what a game of this sort looks like. It's free, it's very good - sort of like a cross between Dust Devils and Legends of Alyria (yet another excellent early Forgite adversial drama game), but with its own angle and a very effortless scenario prep system. The game's relationship map creation is predicated on the characters being enemies with each other, which makes it about as adversial as a cooperative drama game can be.
I downloaded and printed ToE. Thank you so much for bringing it to my attention; I look forward to playing it
The designer of the game, Petteri Hannila, is currently in the process of writing a final game text for publication, so he'll be highly interested in any thoughts and reactions to it from an international audience
I want to plug Shinobigami as being both PvP and storygame...ish. It kinda breaks a lot of classifications. secretly in Love with Player 3. Prevent them from being defeated." etc. And the amount of "XP" everyone gets is based on fulfilling both Mission AND Secret.
Since I'm in a swords 'n sorcery mood again... Blood Red Sands by Ralph Mazza is literally a player-vs-player rpg, in that players are actually competing for the top score to win at the game. You have to play over multiple installments where only one of the players is the current hero, while the others play rival factions. The scoring at the end of a round of installments determine which players' heroes are out and which players get to keep playing their heroes for another round instead.
Hey, what about Agon? I know it's competitive -- I assume that means PvP...
Another vote for Shinobigami
I'm about to Kickstart a game called Blade Bind that's inspired by both Shinobigami and Eternal Contenders. It's GMless and Char vs Char; you can play it as PvP, but it's really aiming for that drama-space rather than "I IZ WINNAR!"-style play. The book's just about ready to go, so it'll be available soon after the campaign ends.
Oh! How could I forget World Wide Wrestling!
@Rafu, if you've played BRS, I would love to hear about it!
It's not, but everything you need to play is in the thread (and there might be some downloadables in the links, as well).