The simplest conflicts don't have any ideology or creeds. It's a matter of two people or factions or nations or whatever who just can't stand the sight of one another. Or they've built up a long history of slights against one another until the net result is the same. Whatever the reason, both sides want the other fundamentally gone. This is Batman against the Joker, Hatfields and McCoys, Autobots and Decepticons. It ends when the other side is gone.
In the strictest sense this doesn't have to be a conflict with a clear villain, even though that's the way it's used most often in fiction. All you really need are people hating one another, which is easy enough to handle over a few perceived or even intentional slights. The downside to having a side without a clear villain is that both sides will sink into that given time. Ideology might get stapled to the conflict after the fact, but the big thing to keep in mind here is that both sides mostly just want to win.
Using this in roleplaying is a good way to really build up enemies, and if you've got two guilds willing to roll with the rivalry aspect, you can have a lot of fun with this. Just take pains to keep an open line of OOC communication between both sides to avoid transferring the in-character conflict to actual player interactions.
Resolution is a bit trickier, mostly because this sort of conflict has to end with only one side. Assuming you don't want to just keep the ongoing feud in stasis, you can always have some external cause force the feuders to put down their arms for a while. Or you could have someone raise the stakes and wind up earning the ire of both sides, breaking unwritten rules in the name of victory.
Sometimes a character will be working against others not out of malice but simply because the other people are there. Con artists, grifters, bandits -- none of them feel any particular animosity toward the people they victimize, just a need to take something that requires someone else having something. A group of bandits waylaying you by the road doesn't care about your life to this point except insofar as it translates into money and items its members can take.
This sort of conflict usually has a clear villain, and in some ways, it's a lot simpler than the former. It's also often handled with NPCs and guest stars because with a clear-cut villain, you really want to be rid of him in the end. You're not going to chase down an insane druid and then welcome her back into your group once you stop her schemes; you're going to cut her into pieces small enough to serve as fish bait.
If you want to play a clear villain in this sort of conflict, OOC communication is key. You want people to understand that you're not being malicious; your character is just trying to do something, and you will likely need to have an exit strategy ending with injury or death. That being said, you can turn things around in the long run, making the grifter who bilked several members of the main group into a long-term member once he's caught and forced to confess.
For NPCs or guest stars, it's a little trickier, mostly because it's harder to give a satisfying resolution when you barely see the head of the snake. It's often better to keep these as low-key or incidental conflicts or to work within the realm of the game's actual content. If you know that there's a boss in a dungeon who can serve as a stand-in for a bandit leader when you want the conflict resolved, for example...
Ain't big enough for the two of us
Sometimes a conflict really is about ideas. Sometimes one side truly believes in something you find utterly reprehensible, and even compromising by leaving one another alone simply isn't an option. You have to eliminate the folks on the other side, they have to eliminate you, and no matter how alike you may be in other ways, there's no common ground to be found.
I'll freely admit that this is my favorite sort of conflict, mostly because it can run hot or cold as necessary without ever shutting off. It's easy for two people who hate one another on purely conceptual terms to put down the feud while it's necessary only to get right back to hatred once a threat has passed. It also allows for situations where both sides are genuinely likable and flawed. There's no right or wrong, just conflicts of ideas.
From an OOC standpoint, this is either the easiest or hardest conflict to make work. Either both of you are on board about what your characters believe or you aren't. If you aren't, or one of you believes that his or her character is right, this is not going to work. If you are, there's not much more to talk about other than hammering out some of the OOC details of how you want things to play out.
The important thing to remember is that while both sides of this conflict are right, they're also both wrong. Victory and resolution is always hollow in this setup, with neither side being the hero against the villain. Just remember that neither side sees it that way.
Want to add something? Feel free to say so in the comments below or via mail to firstname.lastname@example.org. Next week, the importance of working within the medium. The week after that, we'll discuss how to avoid being a tagalong.
Every Friday, Eliot Lefebvre fills a column up with excellent advice on investing money, writing award-winning novels, and being elected to public office. Then he removes all of that, and you're left with Storyboard, which focuses on roleplaying in MMOs. It won't help you get elected, but it will help you pretend you did.