Well. I've played a LOT of MMO's. And some genres I haven't touched at all. But if you want the slightly less typical MMO's:
1: Eve Online. Yes, it's mentioned allready, but I'm going for a complete list here. And EVE Online is both good, and different from any other MMO out there, which is a good thing. The game economy is amazing, and realistic enough you have 'stock market trading'. I had a good laugh the first time I noticed people was investing in minerals to manipulate prices, for instance. That picture earlier with its learning 'curve' being a wall of death was accurate though.
2: City of Heroes/Villains. Superheroes, minimal emphasis on economy / crafting, max emphasis on storyline, cool powers / abilities, and combat. Mainly instanced missions, Uniquely, your starting abilities never get outdated; old abilities improve, new abilities are specialized versions. Almost totally PvE, though, but each enemy type use different tactics, weapons, abilities - leads to you having to adapt a lot, which is fun. I keep returning to this game every once in a while simply because it IS unique. And good. But not something to keep playing for months and months without break. (Currently playing a villain). Most unique 'class': Villain Masterminds.
Trial link: http://www.cityofheroes.com/trial/index.html
3: Istaria (formerly Horizons). Near death, I figure, and quite dated, but a somewhat unique MMORPG - one of the few games where you can actually play a dragon. We're not talking 'draconian' style dragon - basically a guy with scales -either but a huge, blot out the sky, raining fire and brimstone from above kind of dragon. Also, a very nice community, decent events.
Trial link: http://community.istaria.com/pg.php/download
4: Pirates of the Burning Sea. Also clearly different, very good naval combat system, it has ambitions of being an age-of-sail player's Eve online, I suspect; in that regard EvE has it beat in nearly every area EXCEPT that its actual ship combat is much better, and POTBS has an easier learning curve + better PvE. Which is not insignificant details.
Trial link: http://www.burningsea.com/pages/trialKeys/
There's plenty of others out there - honorary mention should go to Tabula Rasa (Currently on deathwatch, they're pulling the plug early next year - kind of sad, tried the trial earlier and it has evolved into a very nice game), Lineage 2, Auto Assault (R.I.P.), Earth and Beyond (R.I.P, long ago), EQ2, Matrix Online, SWG (Whoever's bright idea was it to change the entire system completely halfway through? It's one of the very, very few MMO's that gets WORSE over time instead of better! Every nice feature has gradually been removed! Now it's a balanced generic hell... some changes, yeah, they were necessary, but others? WTF...).