Besides Indian online gaming sites like iBiBo and Zapak, sites like Kongregate and MiniClip host a variety of free online games. You can also try Facebook games. The Facebook App Center enlists some of the best action, adventure and puzzle games for gamers of all ages.
As Anurag2008 suggested, Kongregate and Miniclip are some great ones (personally prefer the former)! Also if you Google what kind of game you want (racing, upgrade, shooter, adventure, platformer, etc) then you'll get even better results ^^