If you have a Facebook account, Many of the games from Playfish are really interesting. They included Facebook versions of Animal Crossing and Big Brain Academy, Mini-golf, Bowling, Geography challenge, and anagram challenge.
Facebook also has Chain Rxn. Rather addicting.
Off of facebook, if you’re into horror games there are is The House and Hotel 626.
If you like escape games, MOTAS is rather fun. The Great Escape series by Mateusz Skutnik and the different [color] Room games on http://www.fasco-csc.com/index_e.php have something too them.
Lastly, the Kingdom of Loathing is a large stick-figure MMORPG that’s a lot of fun.
Edit: Okay, I completely miss-read the question. Missed the 2 player part. Technically you can play things like the Kingdom on Loathing together.