Games (at least resource-intensive ones) are tough to run on any platform other than that for which they were written, which is kind of ironic because a good part of game programming, I am told, consists of trying to bypass the OS as much as possible.
But there are hundreds... maybe thousands of games written for Linux and available for free using Synaptic (in Ubuntu). It all depends on what kind of games you're looking for.
By coincidence, I installed Ubuntu for the two youngest children of one of my best business clients today, on a hand-me-down computer with a trashed Windows system. I didn't count how many games I installed, but there were almost two hundred packages (many of which were libraries or other dependencies) and about 400 MB worth of download by the time I finished selecting -- and those were just the games that I thought little kids would like, which were maybe one-quarter or so of the total available games. All free, by the way.
What's kind of funny is that the kids immediately recognized and knew how to play Planet Penguin Racer, Tux Paint, TuxType, some of the games included in the Child's Play package, and a few of the other games. Apparently either someone has ported the native Linux games to Windows (I know that there's a Windows port of TuxPaint, and that there used to be one of TuxRacer, the predecessor to Planet Penguin), or else one of their friends is running Linux.
Whatever the case, the point is that there's no shortage of native Linux games. Only question is whether they're the games you want to play. I'm not a gamer of any sort, so I'm not much of an authority on the matter. All I know for sure is that it took me almost an hour to scroll through the games and skim the descriptions, decide which ones to install, and install them.
Rich