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Only a few multiplayer games offer live-playing with your friends.

Try Colony and Achievement Unlocked 2

Otherwise you can set up a third-party site for chatting, like Xat or Meebo.

that one operation blacknife game (knife, ops, whatever)
has multiplayer. I think you can set up passwords to join, too.

Try Exit Path, you will be truly addicted to it. >3

Pretty much the only games I have seen with a huge chat is colony, but there is exit path and Alien Girl is right it is super addictive.