What I like about MMO's:
-Scale. Massive worlds. Lots of places to see and explore, lots of content to sift through so I can avoid the parts that bother me and pick up the parts I like without needing to do all of it to move on with the game. (Not all MMO's deliver on this, of course. Champions Online comes to mind. That game feels tiny.)
-Character development. While classes and races tend to be very strict in their paths of progression in most of the MMO's I've played, they tend to include a lot of options anyway. There's usually an "optimal" talent setup for leveling in WoW, but you can mess around with your talents and abilities to make some interesting alternatives if you just fiddle with it enough. Some classes might not feel very different in one tree compared to another (warriors always felt like warriors to me regardless of being fury or arms, though prot's another bag), but going from a feral druid to a balance druid is practically an entire class switch. This is also what I enjoy about leveling up as I like unlocking new abilities and adding them to my current strategies to see what I can improve as I go on.
-Outfitting. What can I say, I like to play dress-up with my characters. Sue me.
-Space to RP. Not everyone does, and this obviously does require other players around somewhat - though it can be amusing to RP on your own with the NPCs in response to their sheer weirdness (much like Shamus's stories do, basically, except writing that humorous little story for your own amusement) - but when it works it can be quite satisfying.
What I dislike about MMO's:
-Required grouping. Yes, I know that second M stands for Multiplayer, which is neat and all, but to be honest, if WoW were an offline game tweaked for solo play - raid content would probably have NPCs included with some altered difficulty/boss abilities to be possible or something, details not important for the moment (since raiding isn't my thing anyway - more on that later) - I'd have probably enjoyed it just as much. Possibly more. Hard to say. On the one hand I wouldn't have had to deal with jerks and strip-miners so I could do what I wanted/needed to get done without people acting as obstacles in my way. On the other I wouldn't have been making friends and socializing during play as I did. The latter point is less significant when considering most of my friends had already quit by the time I left the game, however. Given I was spending a lot of my non-raid time soloing the game anyway I don't think playing it offline would have been a significant change aside from making questing easier due to a lack of competition. And, of course, the AH not being there. That would bite a bit. Alright, that's enough on this topic. Moving on!
-Raiding. I play games to have fun. I don't want to feel obligated to play a game. This transforms fun into a responsibility, which saps the fun out of it. Raiding is less of a game and more of a job. LK Naxx aside (lul), raiding generally requires you to be at the top of your game and focused for several hours at a stretch to be successful. It's tedious, lengthy, monotonous and stressful. All that and you still fail if the rest of your raid isn't up to par. I can't recall how many times my raid team wiped on Archimonde because of people not paying any attention to doomfire crawling toward them, not activating their tears before making little player-sized craters in the ground, not popping potions/healthstones to survive if someone was a second or two late decursing them, etc., and there wasn't anything I could do about that. There were always people behind on DPS who, even after I tried advising them on various ways to improve, never showed significant progress. It was an exercise in frustration trying to complete a goal that, if it was something I could have done alone, I might have been able to do, but being unable to do so because of some team members holding us back. Could I have joined a more serious raid team? Probably, but that would have led to an even more rigorous raid schedule and required leaving behind the people on my team who I liked and with whom I joked around - the people who made raiding bearable at all. Moving to a "serious" raid team would have crushed out any remaining interest in raiding - a self-defeating prospect.
tl;dr - Hate depending on other people to complete personal goals. Extension of point one.
-PvP. I'm sure the basics of this argument are already understood so I'll just say this: it's never balanced, it never will be balanced, and competition with variance in lag is always rage-inducing even in a balanced environment. No thank you. No.
-"Random" quest drops. Someone mentioned this above. If you give me a quest to kill monsters for their organs, make them drop the bloody organs. A quest to kill # of monsters is infinitely preferable to a quest to kill ?# of monsters until they drop # of macguffins to complete the quest unless those items are a 100% chance to drop on each kill. Making them an arbitrary chance to drop is bull - cut it out. At the very least make a maximum kill limit: after X kills you're guaranteed to get all your drops. More than once I've gotten 9/10 items I need only to then get stuck killing upwards of fifty (sadly not exaggerating - sometimes the dice just SUCK) additional monsters to get one more item to finish the quest. It eases the tedium to just think of this as grinding monsters with a bonus waiting at the end, but only a little, and self-discipline of that sort only goes so far. It shouldn't be needed for a game in the first place, of course, given a game is supposed to be fun, yes?
-Endgame in general. I've learned all my class abilities, I've explored the whole map, and seeing the final story-related bosses requires getting upwards of 9 other players of similar power and skill to cooperate with me for hours at a time. All that's left to do is get shinier gear...for no reason, since my current gear is obviously enough to do the available solo content since, well, I'm at the end of it already. Bored now. If only I could see that raid content without needing an entire gang to do it...hm...
Eh...I could probably go on but it'd be getting into nitpicks. That probably covers the broad strokes. I'm indifferent to crafting, for instance: it's more a means to an end than an end in itself for me.