As of 2012 and since a great many years, the most common variant of Poker played in the western world is, and by very far, Texas Hold'em.
In any casino I've been (both in Europe and in the U.S.) "No-Limit Hold'em" was always the most played game. It is also the most commonly played variant on the various online poker sites. It is also the most commonly played poker game when people organize private games. And it's also the most commonly shown poker variant in movies (for example in "Rounders", from 1998, where John Malkovich and Matt Damon battle in several No-Limit Texas Hold'em games) and on TV (including in poker shows).
This can be verified by installing online poker clients and checking the games that are available and the number of tables opened for the various games or by checking any poker show on TV.
Texas Hold'em is by far the most common. Typically it's No-Limit Texas Hold'em ("cap limit" games and "fixed limit" games can be found too, but they're less common). Then there are additional variant, like "cash game" or "tournament", deep-stack or not, with an ante or not (even for cash games), etc.
I guess that many years ago at one point five-card draw was the most common (it's for example quite common in much older movies) but I have no numbers about that.
So to answer your question:
What is the most common variant of poker?
Texas Hold'em. Typically No-Limit Texas Hold'em (both in cash games and in tournaments).