As a DM I am also of a mind that players aren't disallowed from doing with their character whatever they can do. I do not, however, regularly invite players who are not team players, since I like to run a game that is a team game. So, I voted "sometimes" since it can (and has) happened. That just becomes the last thing a player does at my table.
I let the players do whatever they want, including killing themselves. However, I hope they will not complain if some authority begins an investigation.
Almost always. The PCs have a hard enough time surviving against the monsters and NPCs I send after them without having to worry about each other. As DM, though, intra-party conflict is out of my jurisdiction.
It's just like our agreement to not use Evard's Black Tentacles. Nothing was said, but everyone who was there that session knows why.
It's happened before, usually because some misfit doesn't know how to be a team player and cheeses off one or more PCs to the point where violence erupts. Most of the time it ends before anyone actually dies, and in fact the only time I can remember it ending with anyone dying (the offending PC in this case), the player of that character had been AWOL for nearly a month; killing her at that point was purely cathartic on our part.
I pose the question to the players at the start of the campaign. If they all agree to allow PC-killing, then so be it.
The object of the game however, is to have fun, and many players find it less amusing to have their characters slaughtered in the night by so-called compatriots. Especially when it leads to accusations of DM partiality.
So far, no campaign I have run has yet done PC-murdering. Plenty of intraparty strife as it is. Threats of lethal deeds and mock/trial combats have taken place.
At the begining of the campaign, I ask if it is a cooperative game or a competitive game and they vote. Cooperative means there is no PvP actions and they can trust the new PC they meet in the bar to join in their party and not kill everybody the first night he takes watch. Competitive means anything goes. So far they've always chosen cooperative. Even then, through role playing sometimes leads to impass between charac ters. If both characters are willing to the conflict, I do not impede their actions.