We have a rule that any character a player brings in must have a reason to want to cooperate with the party. You may worship the same deity as the cleric, be the warrior's cousin, whatever, but there has to be *something* that makes you joining with the others a logical thing.
Once the party is together, what they do is up to them. The DM doesn't tell them they can't kill one another - that's roleplay. Since it's a roleplaying game, telling others what they can and can't roleplay can easily squash the fun, even if the DM does feel like it's "for their own good".
We had a scenario a while back where I was playing a completely naive little girl. I was lawful good and completely trusted a classmate of mine (PC) who happened to be chaotic neutral (he didn't wear a badge that labeled him as such, you see). We uncovered a plot by an evil necromancer that involved human sacrifice. My character was on his list. The other character had a shot at becoming the necromancer's apprentice if he handed me over. He came to my character and told her the whole story...but then he suggested a way to trap the necromancer that involved drugging my character and using her as bait. Out of character, I knew that the other guy might actually turn my character over to the necromancer, but in character, I trusted the guy completely. This made for a lot of fun between games, and a lot of laughing around the table. (Him: Here, just drink this and let me tie you up... Me: Sure!) In the end, my character was not betrayed and the necromancer was taken out, but not knowing what would happen made things a lot more fun.
I think the point (and what we all seem to agree on) is that we should play to have fun. Whatever is fun for your group is what you should do.
I also think there's a HUGE difference between "allowing one PC to kill another" and full on "PC versus PC" gaming. As has been said several times, just because the DM doesn't disallow it doesn't mean it happens often.
I chose "Always".