I've never been a big fan of player versus player type situations in role-playing games. Now while I may not like it I do understand that there are times when people are not going to agree, and that type of situation can add to a role-playing experience. If everyone gets along and is all happy all the time it can make for a boring role-playing session, the trick I think is to find and strike some kind of balance with your players. Here are some of my thoughts on how best to do that.
One of the first steps you should take is getting everyone on the same page. Talk to your players and find out how they feel about player vs player. This part is best done right at the start, even before they make their characters. It is likely that you will have a mixture of feelings about it but this will, at least, give you a place to start.
Once you have a sense of how everyone feels about player vs player it is time to lay out some ground rules. Depending on what input you got from the players this could be almost anything from the extreme of anything goes, to No hurting, hindering, or even threatening of other players. Most likely you will find some middle ground that is comfortable for all players. One great example of this is a rule from Pathfinder Society play that prevents any character from taking an action that would harm another player without that players permission. It works fairly well however it does sometimes lead to some unrealistic positions within the role-playing game.
I've talked about full blown violence between players but what about the threat of violence. Should that be allowed? In a lot of cases, the threat of violence will lead to full blown violence. My character threatens you into do something, you might just do it initially but afterwards you are going to want revenge for what I did. Which is just going to lead to even more violence between PCs. So even just the threat of violence is going to lead to long-term problems for your campaign that you need to be ready to address and deal with.
One thing of note about all of this is that if you are the GM/DM of the group and you have strong enough feelings on the subject feel free to just make a blanket ruling about it. Just know that it could cost you some players, it might not but that is the chance you take when you make a ruling about the style of play you will allow at your table.
Also, keep in mind there are some games out there where player vs player is not only intended it is actively encouraged. One of my favorite gaming moments was a Dragon Age (By Green Ronin games) game. A large part of the plot had to do with the character morality. Would they turn on the person who hired them for a greater return than what he had offered. So over the course of the adventure the players had little challenges that would allow one of the NPC to gauge their morality depending their actions the PCs may or may not be invited into the plot against the king and be given the opportunity for more money. All but one of the players were deemed immoral enough to receive the offer. When the offer was made to the players they were told that in order for it to work they would have to deal with the one PC who was too moral to be trusted.
The for next little while they were slower to heal him or come to his aid in hopes that nature would take care of him and they wouldn't have to do the deed. In the end, they decided to turn on him. After trading blows for a moment or two our ethical and moral PC realized that the group was after the baron's children and grabbed the nearest one to use as a human shield. With his blade at her throat, he tried to negotiate is way out of the conflict. While I don't recall how it all turned out, I'll never forget my jaw hitting the gaming table when the player took his action to grab the kid.
None of that would have been possible if I had a blanket rule against player vs player at my table. So while I won't every say no 100% to player vs player it is something that I will always take seriously at my table and try and address before any new games begin.
In the end, as players and GMs we all have to decide what level of unrealism we are willing to put up with it. After all, this is a game and we are all here to have a good time. Like I said earlier player vs player situations are all about striking a balance.