Looking at the Stars options, 13 different games are available in tourney form. This treats hi-lo and extra-card variations as different from the main game, but doesn't treat limit, pot-limit and no-limit as separate games. (Nor does it include mixed games.) Some sites spread or have spread other games.
There must be hundreds if not thousands of varieties that have been played, though. People invent poker variants all the time. In the past Party and Full Tilt - and maybe others - have invented their own varieties. Sometimes I have seen threads on this site in which new varieties are invented.