The game I used are Minecraft.
The game is cross-platform (as in, it runs in both Windows and Linux).
Minecraft's F3 button reporting of FPS will be used
The games will be the only additional software running on the system when I make the measurements. The measurements will occur after the game has rendered the game-space.
Fedora 18: 30-40
Ubuntu 12.10: 30-40
Windows 7: 15-25
Windows 8: Not yet tested
Ok, the Linux boxes were all around the same FPS.
Windows 7 lagged considerably, and was almost unplayable.
Gentoo tended to have the best overall, but Fedora was fairly close.
If you do run games on Linux, use Gentoo if you are willing to install it. Otherwise, use Ubuntu for its integration with the Humble Bundle and Steam (upcoming).
Fedora is great, but it doesn't offer anything that a gamer really wants (ease of driver udpates, ease of installation, and frames per second).
Skip Windows 7 for now on intel integrated graphics.