I saw on Massively that the UK newspaper The Guardian is asking its readers to design a virtual world without fantasy or sci-fi. Partly the reason for this article stems from a post by Richard Bartle on Terra Nova asking why the predominant genre for game-like virtual worlds is fantasy.
There are a number of MMOs coming out soon that avoid the fantasy genre: the GTA-inspired All Points Bulletin, Sony's "The Agency," and Pirates of the Burning Sea.
If one considers fantasy to mean only Tolkienesque swords-and-sorcery, the fantastical elements of the horror genre, such as vampires and werewolves, would make a rich backdrop for a virtual world. A Torchwood or Doctor Who based game would make great settings as well; while they involve sci-fi, these shows aren't about spaceships and phaser pistols. But all of those settings could still be considered fantasy if you broaden the definition beyond Tolkien.
There are plenty of other possibilities for an MMORPG, even if you eschew anything supernatural, futuristic, or fantastical in any way. Early 20th century mobsters could make an exciting (though probably controversial) backdrop for a virtual world. The Wild West is another obvious choice for a setting.
One setting I'd like to see turned into a virtual world would be one based on the notion of running modern-day corporations. For an idea of how that would manifest itself in a game, you might start with a game like Stardock's The Corporate Machine, except, of course, make it massive and multiplayer. And with places you could run an avatar around.
Each "guild" would be a corporation and players would assume various roles in marketing, public relations, research and development, and so on. The gameplay itself would manifest itself mostly in the form of card games, like Legends of Norrath, or the diplomacy system in Vanguard. At some point, the game would end (that's not so far fetched, A Tale in the Desert is an MMORPG that ends!) and the server would restart. By allowing the server to restart, the game stays fresh and able to welcome new players (most current MMORPGs have a hard time attracting new players once they have aged, since all the existing players are high level and the new players have no one to play with.)
I suppose it wouldn't be a virtual world if you couldn't run around in it, so part of the game would take place in a surreal office. Instead of completing quests, you have to handle "situations". (I hate it when we have a "situation" at work.) An example situation would include discovering that the coffee machine broke down; this would cause NPC staff to fall asleep. If left unchecked, the corporation's productivity will decline. Another situation: the media shows up unexpectedly, and someone needs to hype the unfinished product to them. The corporation would be given a day or two to handle the situation (by delegating the task to one or more persons in guild) or else consequences occur. Situations would also allow multiple solutions with ethical dilemmas. PVP would occur in the form of corporate espionage.
Corporate progress would be measured in the usual ways: dollars and market share, both overall and within the corporation's chosen industry. Players would earn salaries based on how desired their skill sets are (based on how effectively they overcome the "situations" that the corporation faces), and they could defect to other corporations if they wanted.
What type of virtual world would YOU build, if you couldn't use fantastical elements at all?