Have you heard of pocket ninja? If you are a fan of Naruta or Bleach you will love this game. A lot of online users are getting addicted to it already and having fun as well.
Or try backyard monster, it is a strategic game that needs you to build a certain base that needs to be upgrade. You need to build your defenses so other players can't attack you and robbed your resources. You can also build soldiers to attack and steal their resources too.
If you are into tower defenses, there are a lot of free games online. You don't have to download them.
Or try facebook games, they are also good and you can interact with different people too.