Edit Wars, aka Wiki Wars are the unfortunate occurrence when two or more people fight over edits to an entry. While accidents do happen, it's always a good idea to be polite about your edits and follow the Wiki Ethics guidelines to avoid an Edit War. When Edit Wars happen neither side is happy and the people who are left to clean up the mess are even less happy. In short, nobody wins.
You can create a separate talk page in the case of an edit war to facilitate discussion and so that no one reverts over the discussion. Insert [[stop]] into the page, and create the new talk page. If the insertion of a controversial edit is the motivation of the edit war, move the questionable material onto the talk page. You can use the talk page to list multiple versions of the controversial edit, and after discussion and editing, the community can decide which version is best.
More info on Edit Wars: Edit Wars
When you get involved in an Edit War, please try using Exponential Backoff Editing. When you're pissed off and in an edit war, consider taking a Wiki Chill Pill and coming back later. Keep in mind that when you're upset, you'll probably be a better writer tomorrow.
When the war is over and the issues are resolved, the /Talk page should be deleted. Wait a day longer than seems necessary before deleting it, though. An extra day won't hurt, and it'll make people feel good to get in one last comment.
Some previous edit wars are cataloged with lessons learned from them.