<span class="bold">Urban Dead</span> - An MMO board game with RPG elements, similar to Vampires! but with a deep ruleset and shittons of drama owed to the fact that players basically have total freedom. There are organized zombie hordes and survivor factions, "feral" hordes usually directed around by whoever is most fluent in zombie groaning, roaming PKers, groups organized to hunt them, hospitals staffed by roleplayers, death cultists who spy for the zombies, zombies who help survivors, and countless specialty groups. I usually run with a group that maintains an open revive clinic for zombies with brain rot who can't get revived anyplace else. No graphics to speak of but there's a Firefox addon that adds map artwork so you aren't just looking at a grid of building and street names. This has been my favorite game for years.
<span class="bold">Dofus</span> - A cute Japanese MMO with a decent size free area and turn based combat. I happen not to like it, but it has a huge player base so maybe they are doing something right. It's got charm, I'll give it that. (Reinstalling it now actually.)
Edit: Dofus is French. I was thinking of StoneAge 2, which I would rather have suggested but I think it's dead. <span class="bold">Wizard 101</span> - A kids' MMO easily clumped in with garbage like Toontown Online and Free Realms, it's really a turn-based card game, and it's great. You fight monsters on a sort of rune-board-thing on the ground, and random people can join you at any time. PvP is done in ranked matches which can be very long and are often rather harrowing. Best of all there's a minimum of drama and other MMO BS because half the players are so young they aren't allowed to use the chat system, and people can't really bitch about what you do in combat because hey, your hand sucked. Another subscription thing but with a pretty large free area and unlimited use of the unranked PvP system. I spent two months earlier this year playing nothing but this game.
<span class="bold">Stone Soup</span> - A roguelike not quite as serious or respectable as Nethack, but more fun in my view because it's designed to give you a fair shot most of the time and to prevent grinding. I usually prefer straight up ascii for my roguelikes, but the tiles version of Stone Soup has an automap and inventory with icons and mouseover information, which is handy at least while you're (re)learning the keys for everything.
Thanks to the others posting recommendations here as many of these are new to me.