I noticed two levels of "going against the party" here. One is where the character simply has different goals from the party and follows his own agenda, and the other, is PC fratricide. PC fratricide is ok in a short game because once it happens, trust me, the game will be short! If a PC has different goals from the party, and follows them, that's fine but the DM will have to ensure that what that PC does can still mesh with the party for most part. Classic example I can think of is Raistlin in Dragonlance. Of course, there'll come a time when the PC is nearing his goal and this would require him to split completely from the party. How this happens and how it is managed so that all the PCs can have an enjoyable game falls greatly on the DM.

Personally, I've had bad experiences with the "player who goes against party" syndrome, because I used to play in a group where the player who does that all the time is a munchkin. He will always play the fighter-dual mage (just to get the hit points) who wants to become a lich. This happens no matter what D&D campaign we're playing. And when it looks like he's not able to achieve his goal, he'll throw a tantrum and quit the game. Or the players get so fed up with his whining at the DM, they quit the game. I've no doubt that mature players and a mature DM can create a campaign where a player can go against the group and everyone still has fun. But I've yet to see it.