It kind of depends. I don't enjoy MMOs, and the co-op mode of some RPGs is fine in principle, but among my friends and our lives I don't find it very practical.
What I do occasionally get into is brief tactical or sports games, where you have a session, and that's the end of it. Even before online play, my earliest experiences of really great two-player video games were the EA Sports titles on the Megadrive. I mean, we had really great late nights having championships with the original NHL and Madden.