In my experience, many PbP players seem to have a tendency to lean towards characters that are lone-wolf types who don't get along well with others. Nothing wrong with that; its a standard trope that tends to fit most genres well; it just doesn't always lend itself to great party dynamics; especially when there are multiple lone wolves...

I have experienced bickering, in-fighting and complaining from players (ooc) and characters (ic) in my own games and in others I have played in or read and I found its generally best that the DM/GM put an end to it when it threatens to derail the game or is repeatedly ruining the fun for someone.

I think the best suggestion so far has been to put them in a difficult situation where they need to work together to get free. That's a real unifying storyline, shows them they can depend on each other even if they don't like each other, and makes them appreciate each others value more. Were I DMing such a scenario, I would probably use covert methods of reward and punishment to encourage them to work together. The brash fighter who breaks free first and refuses to help his companions gets hit by a trap that the rogue could have spotted, the spellcaster who thinks he's better than anybody get in a fight with something that can dispel magic, that sort of thing. And of course when they do work together, make the results more successful. If one character 'aids' another on a skill check, have it go down perfectly.

It would mean fudging rolls and a bit of railroading, but you only need to do it for a little while for the players to figure out that it's in the best interests of their HP to work together.

Edit Question: Is it the players who aren't cooperating, or just their characters? If it's just the characters, I would use the above method, but if there are problems between the players (lack of mutual respect, animosity, rivalries) then a whole different approach is needed.

Also consider that the problem may not merely be between the players, but with them.

If this is true:

Then so is this:

Otherwise, letting them know that their intra-party conflict is getting out of hand should be enough to correct things.

I should add, as long as the players get along and like each other as people, it may be that they are working their characters towards that end in their own storytelling. One of the longest campaigns I was ever in started with a bunch of characters who couldn't stand each other. Things turned violent more than once, especially between the two sorcerers in the group, both of which considered the other to be absolutely useless and beneath them. We even went so far as to break up, force our leadership on some rival orc tribes, and go to war against each other. But by the end of the campaign we had figured out how to make the characters work together and they really gelled as a group. In the end, the story of how we came together was more interesting and dramatic than anything else we accomplished.

So I guess my point is that if you trust your players, maybe some backstabbing will be fine in the long run.

I was dead serious with my comment. I have found that players who love Chaotic Evil make great paranoia games.