Are you wanting to play online or offline?
Some great free online games that dont require high specs to get into are League of Legends awesome RTS
Dungeon Fighter online classic beat em up rpg
ijji gunz 3rd person shoot requires a lot of skill but is always flooded with hackers every other patch.
Quake live its like quake 3 but free and launches from the browser.
Offline game I can't recommend since I don't really play.