Star Wars Galaxies.
If you've played it, especially preNGE and preCU, you know what I'm talking about.
If you've never played it, it would take way too much text to fully explain why. It's an MMO, after all.
Ending there would make this post a pointless contribution, so here's a quick synopsis:
SWG was a rather unique Star Wars game in that it did not cast the player as some legendary hero or villian. The game [for a while] did not even let you start as Jedi. Instead, players were simply rank-and-file Joes from the cantina. Players could choose to abstain from combat entirely and instead focus on crafting and mercantile professions. When you saw another player in a city, you really couldn't be sure what they were up to. You couldn't say "this person is level X, so they will go grind Y mobs for XP now." Everyone had their own goals, their own plans, their own agendas.
This kind of world brought a whole different vibrance and perspective to the Star Wars universe. For once we got to see and experience what a 'normal' life would be like, without lightsabers or Jedi or Sith.
Unfortunately, this world was also buggy, unbalanced, and devoid of content. SOE's execution of this brilliant idea was nothing short of horrific. The execution was so bad that it scared developers away from using the game's concept in other titles.
Fun Fact: The wasted potential of SWG sparked a 25 page thread on Penny Arcade [http://forums.penny-arcade.com/showthread.php?t=83801] discussing the same topic as this thread.