There are a whole lot of you, and antagonists are few. If you want conflict RP, you're going to have to avoid being overzealous and stumble a time or two. My advice is as follows:

  • RP isn't a game you're trying to win. This is an interactive story, a multi-author novel, that requires a bit of give and take. The point here is the journey of the character, and sometimes that means failing against an antagonist. When you catch wind of an antagonist, don't immediately go out to crush them under your heel. Even if you're playing a zealous character who wouldn't abide the antagonist in question, there are ways of massaging that. Don't rush to win at the first sign of trouble. There's very little character growth as a result besides a notch in the belt.
  • What doesn't kill you makes you stronger. If an antagonist approaches you with an offer to RP a bit of conflict, don't immediately turn them down. Consider what it would bring to your character; you may be able to explore avenues you haven't before. If, after considering it, you feel it won't bring you something that interests you or you're not comfortable with it, turn it down, by all means. Just don't reject out of hand.
  • The antagonist's life is worth just as much as your own. This is a point in no way related to what the character thinks, but rather a note of RP respect. You would likely be affronted at the thought of someone wanting to kill your character off; just because Joe Evilbritches is playing someone on the darker side of grey does not make him a more expendable character. He has just as much right to play as you do, and you should play with that in mind.
  • Get other people involved, but avoid mob mentality. Friends, guildmates, all those wonderful acquaintances can and should be involved in a conflict plot in some capacity. However, the more people get involved, the likelier it will be that the plot will devolve into baser acts and motivations. Too many cooks can spoil the broth. Just be mindful of it.
  • Maintain the IC/OOC line. Just like the antagonists, you need to keep OOC knowledge OOC. If someone else has been taken to his secret volcano lair and only they know where it is but they're chatting about it in the OOC channel, don't just "stumble by" the out-of-the-way island off the coast. If you don't have an IC reason to go somewhere/say something/do something related to OOC knowledge you have about the plot, don't.
  • Communicate with your neighborhood antagonist OOCly. Have an idea? Not comfortable with where things are going? Want to work together for a more interesting angle? Approach the antagonist's player OOCly and talk. It may spoil a small portion of the surprise, but the ultimate result will be more satisfying.
  • A resolution to the conflict does not necessarily mean the death of the antagonist. Things should come to some sort of end at some point, a conclusion that feels satisfying enough, but there are other ways besides killing an individual. Work with the others in the plot to bring a resolution that works for everyone.

Credit for the original writeup goes to 'No' from Thorium Brotherhood.