One of the major problems of a game in which you can do anything is that... well, there's not necessarily much of a reason to do anything. That's a Terrible Idea recently had an interesting piece on the difficulty of generating goals and objectives in MMOs, especially in contrast with single-player games where your goals are equally pre-generated. The difference, as the article notes, is that single-player games have individual characters with a large impact on the game world. There's no issue of making quests compatible with a wide variety of characters of different races and classes, until the individual motivations and goals can no longer fit into the equation. You don't have anything but the end of content to shoot for.
So what's the answer? The original post notes that it's not really possible to reconcile anything but achievement-oriented goals within MMOs due to the fact that the character will still inhabit a static world no matter what you do. Certainly, there are attempts to create larger-scale impacts for individual characters, but so long as every character goes through the same content or has the same opportunities, there's less of a sense of distinct accomplishment. Player-generated content in games such as City of Heroes offers an opportunity for a different path for each character, but there's still not much of a difference in the actual process. Procedural generation is also bandied about as a solution to the issue, though it lacks any truly successful implementation at this point. Is there even a solution, or is this simply part of the weakness of the genre?