It's hard to say. Generally, I am only going to spend about 20 - 30 minutes there, so it should be short and simple, but addictive.

I'm also a console gamer, but I don't expect an online game to come anywhere near the Xbox 360 games. It's a totally different experience.

Definately Addictivity (is that a word? lol)

I think you need interaction with other users. even just a high score table is fine.

Really? That's fascinating, and would never have occurred to me as a criterion.

First thing, the game has to be rich. I don't want to play two weeks and get bored because I already discovered everything in the game.

Then, it has to be easy to start with. A clear and ergonomic interface is mandatory. There are a lot of nice games on the web that greatly suffer from their messy interface...

A good game needs a beautiful desing. Being a masterpiece is not mandatory, but the design has to be coherent and soft to the eye.

Last but not least, a good game need to offer a wide range of difficulty levels. By this I mean that new players can play and success easily, but advanced players can elaborate deep strategies and find a well-balanced difficulty at their level. The game has to remain a challenge even if you are the best and/or oldest player.