I'm mainly only after web-based games that have some sort of element that encourages you to come back regularly and tinker with it a bit. Games that I do play / have played and like(d) are:
Estiah - a sort of deck-building RPG. This game is pretty fun. You have a limited number of things you can do each day and it takes about 15 or so minutes to do those things, then you basically need to go away until tomorrow. I like that!
Elements - a Magic : The Gathering-type deck-building fantasy game. I've played this for going on 2 years.
Astro Empires - a truly great space-based exploration and combat game. The problem with this game is it becomes a game where you can't really play by yourself, you have to get involved in large guilds/clans and wage galactic war or you get annihilated very quickly in the crossfire. So in other words, you get forced into a style of play. I played this for almost a year though.
Lord of Ultima - relative nice mix of city building and some simple combat. This isn't a bad game, it just didn't keep my interest.
I love these small web games. I want a game that encourages me to login every day, do a little bit, and then go away. I don't want to be absorbed in an endless game (spent 6 years of my life playing WoW every day, had enough of that) .
Please offer up some suggestions of things you guys like. Maybe my suggestions will give you some ideas.
Heavy preference given to games that are free. AstroEmpires is an example of a game which has a free component but after you exhaust that you really get stuck in unable to enjoy the game without paying.
Die2nite turn based zombie survival game.