I'll say that 99% of party drama can be prevented before the game begins, both in terms of problems with the GM, and with each other.
A lot of the problems with RPGs start when the GM just lets the players come up with whatever kinds of characters they think are cool and want to RP with minimal input other than to maybe guide things in the direction of a balanced party (making sure you have someone who can heal for example). Sometimes this works, but more often than not it leads to people going to the extremes of their personality types without looking for any middle ground or how these characters are going to interreact. While in a fantasy novel, clashing personalities among friends and comrade can be fun, in an RPG things tend to be a bit differant, especially seeing as there is more than a bit of interesting verbal interplay at stake, certain types of behavior can have direct repercussions on specific character types. Not behaving in a certain way, or doing something by consensus can lead to characters taking penelties, losing class abillities, and all manner of things.
To put things into perspective, if someone is playing a character like a Second Edition Dwarven Battlerager, or some of the warrior "specialty priests", a lot of RP is a foregone conclusion because it would be bad RP for these guys to negotiate much. What's more stealth and guile is likely to be a foregone conclusion because especially in the case of some of the War Priests, walking up and calling out their enemy is how they are supposed to behave, and dying is not viewed as being a bad thing. If someone builds a bard based around stealth, guile, and negotiation he's in for misery because he represents the anti-thesis to that school of play and both characters are going to lose out if they concede to let him to do his thing very often. On the other hand a more militant bard who also walks in the front door like a Skald or whatever might work, as would some kind of rogue mostly based on say trap detection and lock picking rather than sneaking around.
As a GM problems also occur when you have a specific type of campaign in mind, but don't give people much indication as to the theme, and the players wind up making characters that don't work with it. An anti-social dungeon crawling party with say Dwarven Battleragers and such is not going to work well in an urbane, intrigue based game, based around confronting a group like the Forgotten Realms "Night Masks". On the other hand really social characters based around the idea of RP and getting everyone to like them and give them information are going to be an unfun liability if say the campaign involves crawling through Undermountain in search of loot where the highest form of likely socialization involves what choice of curse word to use as you clear out the latest room with your attacks.
I know many people disagree with me, but typically the most functiona advice I give new GMs and those with problems (and have gotten praise for) is party planning. Don't let your players show up and drop a sheet on you too often if they have no idea about the campaign. Also give the players some indication as to what the focus of the campaign is (and if your doing it right, you should have planned it out somewhat) is it mostly set outdoors, in a city, does it involve heavy dungeon crawling? You don't need to be specific on the plot, but telling players that the game is based around certain elements or has a specific starting location can save a lot of headaches.
What's more, while you shouldn't assign characters, make sure the characters are at least somewhat compadible. You don't want to have a constant push-pull relationship going on due to character roles. Role-playing is one thing, but if you for example want your game to involve stealth and negotiation with enemies, chances are you should tell the guy who wants to play a Samurai, or a character who abides by something like the first edition D&D "Cavalier" code of honor to pick something a little more limiting, or at least something that won't risk losing their abillities if they don't scream "death before dishonor" and attack anything evil by running up to it directly as a true warrior should (and for those who argue that this is stupid, I will point out that this is how the books define these characters, and all those special abillities are given to them to help them survive that kind of idiocy). By the same token if someone is wanting to play a character like an "Urban Avenger" and you plan to start the game in an isolated hamlet, with the adventure largely revolving around battling ice trolls in their cave... well you might want to veto that one too and recommend something else.
I probably don't express this well, and make it sound a lot more draconian than I actually intend, but the bottom line is communication. Have everyone generate their characters together as much as possible, head off as many problems as you can see before the game starts, and you'll have a much smoother time of things. Not a lot can be done for player personality traits, or even character RP, but these things can be limited from becoming problems by at least removing problems that stem from issues tied to game mechanics. It depends on the game and edition, but basically a clerics have to follow their dictated ethos and the rules of their specific priesthood, paladins have to stay good, Samurai have to behave with honor and will not generally attack through the back door (history aside, the D&D version is usually written that way), Cavaliers always attack the strongest opponent and generally do not negotiate with the enemym in all of those cases violating those rules can strip a character of their special abillities (as mentioned above). Prevent things like this if they work against your game and the other players, and then it comes totally down to style and becomes much easier to deal with since your less likely to run into irresolvable conflicts where someone is going to get their character gimped no matter what they do.