I'm going to go against the grain of most other responses and say that, heck yes, I allow it. I might interfere if I think it will be fun to do so within the campaign, but I won't stop one PC from killing another.
I do expect my players to come up with PCs that are motivated toward cooperating with each other and not fighting each other, but beyond that, they can play what and how they want to play. If a PC killing fits in with the characters as they've been played, I have absolutely no trouble with it.
For example, in an Orient Adventures campaign I ran many years ago, we were playing in Blood of the Yakuza, a module designed to bring out political rivalries and conflict between PCs due to competing allegiances. The a couple of barbarians (brother and sister) had a magic ring that was pilfered by the party yakuza while they had it out on loan to the monk. It was a ring of invisibility and the only real reason the male barbarian kept it was because of the player's metagame thoughts on the topic of giving a ring of invisibility to a rogue. The monk resolved the situation peacefully by paying a friendly street urchin to steal the ring back. The barbarians, noses out of joint, ratted out the yakuza (who was also ninja) to the localy daimyo. WHOO BOY!
Once the yakuza PC got wind of what happened (don't assume a yakuza doesn't have the right contacts to figure things out, word to the wise), he faked his own death with the help of some other PCs, went into hiding, and came back under a disguise and rejoined the group. He plotted the whole spring term to kill the barbarians, I interfered a little to draw out the drama, but he succeeded in the end.
At first I thought this was a problem and, during a semester break, I consulted with long time friends and other players. All of them, unanimously, asked my why the barbarians were still alive in the first place. You see, where I come from, gaming wise, a little pilfering is OK, especially if dealt with peacefully (as this was). But betraying members of the party to certain death? Beyond the pale. PC death was the agreed upon penalty... assuming the yakuza PC could bring it off.
Did the barbarian players get their noses out of joint? A bit, but I can't say they didn't deserve the treatment they got.