My son and daughter normally get along very well but, they do have their American Gladiator moments.
On the rare occasions that they argue and snipe at each other, I stay back and just let it run its course. It's important for them to learn how to resolve conflict on their own and if I step in to referee every time they raise their voices, they'll never learn for themselves.
If the arguments become too heated, I use the following trick: I send them both into the same room, tell them that they can't come out until they've worked it out and then I shut the door. This usually helps them to resolve the issue within a few minutes so that they no longer have to sit in the room together.
Too bad we can't use this method with the adults in our lives who don't see eye-to-eye.