Ostensibly MMORPGs are about playing a role and making friends/enemies online. The reality is it's usually a level/skill grind dressed up with lore few care about or bother reading. A few like Ultima Online or EVE give players more freedom that can result in interesting dynamics. http://www.escapistmagazine.com/issue/25/5 The big trend in the last few years has been a move towards more individual play with more and more instanced content, doing away with the whole "massively multiplayer" aspect that supposedly defines the genre. To find the kind of social interaction promised by MMORPGs you have to turn to text-based MUDs.

Then there's the non-RPG MMOs like World War 2 Online. It's a 1/2 scale recreation of the western front in a combination of FPS and vehicle simulations. Axis and Allies fight until one side captures all the terrain(which may take several weeks or months), then the map resets and the game starts over. The other side of that coin would be Planetside, another MMOFPS, but designed to remain in a perpetual stalemate. Players can take enemy territory, but keeping it is made difficult enough to not allow the fronts to shift permanently.

Outside of the games centered around combat are ones like A Tale in the Desert where the emphasis is on building things and competitive creative expression. Second Life takes it to an extreme, where there is no "game" but what objects the players build and how they program their creations to interact with the world.