There are many high quality online fighting games that have a loyal fan base. Capcom's popular fighting games include Ultra Street Fighter IV, Ultimate Marvel vs Capcom 3, and Street Fighter vs Tekken. Some other great titles are Skullgirls, Killer Instinct, King of Fighters XIII, and Mortal Kombat X.
A terrific source for online fighting games is Shoryuken.com, which is a website dedicated to the fighting game community. You will find updates on current and upcoming games, as well as a list of upcoming tournaments in your area. The forums are also a great place to discuss strategies and tactics for games you are currently playing.