The reason i like mmo's so much is basicly because of the RPG part.
I really like/enjoy exploring big open worlds.
To me mmo's are just RPG's with the exception there is a lot more stuff to do, there are actual people in the same world and the game basicly never ends.
With most RPG's you're eventually going to run out of things to do and unless there are mods (like for example Oblivion) for the game you are done. True you could run out of stuff to do in an mmo, but for me that has never happened.
The other people playing the mmo with you make it more fun to run an instance more than once, something i would hardly do when playing an (singleplayer) RPG.
One of the things i also enjoy is the feeling of a "living" world where stuff changes according to actions in game, unfortianatly we don't see that much in MMO's, one thing does come to mind that was somewhat of a living world and that was Tabula Rasa where you would have several bases that would fall into enemy hands without players fighting for it, the bases were under constant attack and if the players would loose the enemy took over and players would have to fight to get it back.
I really enjoyed this and i could often be found fighting or defending these bases instead of questing.
You could argue wether this is actually changing the world, but to me it felt that way, it felt like i was making a difference when taking over the base was a success and my allies took over the base.
Maybe it is also a bit of a negative that i like RPG's so much as i often do spend most of my time in mmo's playing solo and only group up with other people when i have to for dungeons etc, even still i would rather level up and take a mob that i couldn't beat solo at later level, basicly out leveling the mob.
As a result of course i don't get to raiding content, mostly because of the elite attitude of a large percent of the player population demanding you to have x amounts of achievements and certain gear.
The random dungeon finder in World of Warcraft is of course a great tool for getting into dungeons and experience that side of the game without that elitism and i do enjoy using it and have fun trying to get through a dungeon.
But more often than not i return to solo play because i simply enjoy exploring, going into new areas, go see what's behind that mountain over there, discover great scenery/views, i love getting completely immersed in the world i am exploring and have a feeling i made a difference in the end.