As long as people role-play their characters within the established context of their history, personality, and motivations, we all could care less what the others do.
(what follows is a tale of vendetta and death, player versus player. Read if you like, skip if you want. This is an evil-heavy party.)
My second character with my current group was Bilune, a CN bard. He was in the adventure business for personal profit, plain and simple. He also was something of a womanizer, because he was just so good looking (according to him) that any and all women should be honored by his attention.
He rubbed one character wrong from the very beginning: Crimson, the prostitute-turned-Assassin (who, incidentally, is played by the wife of the DM). My character was crude and derogatory, making frequent remarks about her appearance (comely) and what they could do together that night, etc... Slowly, Crimson went from dislike of Bilune to outright, open hatred. She tried to kill him on multiple occasions, but he always slipped the noose, laughing. He considered himself invincible, and didn't give a damn what other people thought. He pretended her attempts were akin to mild flirtations, which enraged her. Otherwise, Bilune's min-maxed Perform and Diplomacy served us well in the city-based campaign, as did his Wand of Invisibity Sphere. He was, unquestionably, an asset to the group, if you could put up with him. But she couldn't.
Finally, Crimson snapped. There was a dispute about what to do with some powerful items we'd found on another plane - each of which would strengthen the power of an individual god if returned to our home plane. Everybody else wanted to pick and choose which item (and therefore which god) they wanted to support. Bilune wanted to take all the items and sell them off to the highest bidder, be that the clergy in question or an opposing clergy, and he outright stated that he didn't care one bit which gods became more powerful as long as he got his money.
Crimson death-attacked him, but he made his save and lived. Unfortunately, the poison on the blade dropped him to ONE point of Con. Despite his sudden lack of hp, he managed to take down Crimson with his own ace-up-his-sleeve - an Arrow of Slaying (Humanoid). The rest of the party, not having witnessed the Death Attack, turned and killed Bilune, enraged that he should so senselessly slay a member of the party.
The cleric did a few Speak With Deads and determined what had really happened, and we were both raised with the requirement that we both be nice to each other now. We both agreed out loud, but of course neither of us had any intention of letting this vendetta die. Crimson, though, was more on-the-ball than was my poor bard.
Later that same session, Bilune was performing for the Royal Court a complex dance/castanet gig. Unbeknownst to him, Crimson was lurking behind the curtain, inches away. The subsequent Death Attack killed him outright, in plain view of the Royal Family, with hundreds of witnesses. Yet Crimson, still hidden behind the curtain, managed to get away unseen. It remains, to this date, one of her crowning achievements as an Assassin, a feat not easily matched. Bilune elected not to be raised, since that was the way he would have chosen to die - performing the best performace of his life before royalty.
I should note that I found this session to be incredibly fun. It's the only time my character has died twice in the same session - and the DM didn't even have to plan any encounters. The player of Crimson and I get along just fine, as we always have. (also, my new character gets along with Crimson just fine (he's a min-maxed NE archer, with a Shadow Sniper PrC from the 'net). He's homicidally insane and cares for nothing but mastering his ability to kill with his bow from hiding.)
I'd just like to say that, with the right group of people, role-playing intra-party conflict is almost the best part of the game. People don't get along perfectly in RL, and neither should well-thought-out characters in an RPG. I should mention, though, that our level of role-playing often almost reaches the level of improvisational acting, where we try as hard as we can to put ourselves in the shoes of a character who is fundamentally unlike our actual selves, trying to give their personality and actions true depth and meaning. This might not be the way most of you play D&D, but it's what we like, and at the end of the night, there are no hard feelings. What's said and done in-character stays in the game, and has no out-of-game consequences.
It's really just a game, after all.
