The most common game variants are no-limit Texas Hold’em (NLHE) and pot-limit Omaha (PLO).
Every single site will have a multitude of NLHE games running at any one time. Even if the site is small, there will be several options for hold’em players to get into the action.
PLO is also quite popular for sites to offer. If a site has the ability to offer more than one game, Omaha will certainly be the follow-up to NLHE.
Otherwise, the variants offered can be anything that the site chooses to highlight.
Other sites might offer limit versions of hold’em, the hi-lo variant of Omaha, or various types of seven-card stud. Some sites even create their own games for a limited release.