Two Free Games -- Operation7, and Project Torque
About each game:
Operation7 - Operation7 is much like any other free online FPS, except that you can lean, weapons are permanent, and you can customize every aspect of the weapon (barrel, stock, scope, clips, and more...).
Operation7 Main Website: http://op7.netgame.com/under18/
Project Torque - A free online/offline racing game with many vehicles and customization options. This game features online and offline play (but you require a connection in order to play). In this game, there are actually damage models (like you'd see in many modern commercial racing games).
Project Torque Main Website: http://project-torque.aeriagames.com/
Here's a couple other recommended games to try out (none of these videos are mine):
Combat Arms: • Combat Arms (Gameplay)
F.E.A.R. Combat: • F.E.A.R. Combat gameplay
America's Army: • America's Army 3 - New Features (HD)
Also, look out for Q4 of this year, for Need For Speed: World Online, also free, but just as good as any other Need For Speed.
Here's a link to the video for NFS: WO: • Video