Check out WineX actually. It provides DirectX compatability layer, and installer tools to get past restristrictions that get put on installation CDs by the companies.
Basicly you pay them 15 dollars for 3 month subscription (at least last time I checked, things at their website seemed to have changed quite a bit.). During that period you have a vote on things like what games to concitrate on supporting next, and other policies. You get unlimited downloads and updates to take advantage of the new features..
On a scale of 1 to 10 were 10 is easy and 1 is hard, the WineX is about a 7-8 for people new to Linux.
check out this Game compatability lists
Games that are a 5 work perfectly. 4 stars have minor issues (like a menu is scambled or cutscenes or music doesn't work sometimes). 3 stars are pretty iffy, anything below that is worthless.
Depending on the Game you may see a big or a small performance hit. Lots of games may require DirectX and special install support, but for the actual game they use OpenGL so that you still get good performance under WineX (or Cedega, now I guess), other games that are pure directX will see a larger performance hit.
Also lots of popular games do have Linux versions. Doom3 will have a linux version, I play Ut2004 natively for example.
Linux Games
Linux Game Tome (personal favorite)
LinuX-Gamers
Also there are about a gazillion little homemade Linux games that are fun and are free.