I find none of these particularly good, but perhaps they are worth a look. Runescape would be my favourite, and neopets would be my least.
www.runescape.com - runescape
Basic Run-down: a 3d adventure where you can interact with other people. You can fight, mine, craft and stuff. You can build on your character's skill to make them better at stuff.
www.neopets.com - neopets
Basic Run-down: a world at your fingertips, where you can make money, build on your pets to make them fight, talk with other people, etc. Lots of games, and perhaps the worst administrative team in the history of the universe.
www.battleon.com - adventurequest
I haven't played this much, but I figured it might be woth a look. You fight in turn based combat against enemies, and can visit places to buy weapons and what-not. No interaction with other users.
www.ogame.org - ogame
I quite like this. It's a text-based space sim, where you are given a planet, and have to build up your colony and even expand to new planets. You can wage a war in space against other players, but the computer calculates who wins. It's a log-on and update my colony game, you wouldn't sit and play all day.
Feel free to comment.