http://www.tetrisfriends.com/
It's like competitive battle Tetris. You make an account and start playing against other people, simple as that. You can either race others to complete so many lines (clearing them) or you can play the battle mode in which you can complete more than one line at a time (Doubles, triples, or 4 lines at once is called a Tetris!) it adds lines to your opponent(s). Battle mode comes in 2 players or 6 players.
There's no chat room or anything far as I can tell, but still hella fun. I've played 14 games at the moment and have ranked first in 13 of them. I've only played 6 player battle mode so far, since it seems the most fun.