I think bughouse is the most popular of chess variants (if you don't count national variants like Xiangi or Shogi). It is usually played by 4 people, but I think 2-player version should be fun as well.
(hide) If you click on a person's name and then click Finished games you will have a list of games that have been completed, then click on the name of the game to get a summary of all of these games, then click on the name of the game again and you will have a game to view and analyze. (Servant) (show all tips)