I don't really know if this qualifies as a MMORPG, exactly--it's kind of a hybrid of MMORPG (lite) and social networking game.
Welcome to PokéFarm! - PokéFarm
Pokefarm is a site where you play the role of a Pokemon breeder, rather than a Pokemon trainer. You adopt Pokemon eggs, hatch them, and raise your Pokemon. The way you hatch the eggs and level your Pokemon is by interaction--you "click" on other people's eggs/Pokemon (which gives them hatching/leveling points) and then those people "click" your eggs/Pokemon. There are also quests, special events with items or unique Pokemon, and the Dreamworld--a web-based version of the Pokemon game!
I really love this site. I'm not sure if it was the first "adoptables" website, but it certainly was *one* of the first. The creator is busy adding more content all the time. It may not have the same level of complexity and depth as a typical MMORPG, but it is surprisingly addictive.
Most of the folks on there are either college aged, or teens; but there are a few of us older gamers on the site. I am attempting to start a clan for those who are over 30. If you're interested, send me a PM and I'll tell you more about it.