I like cartoony graphics with bright, contrasting colors like WoW. It's more pleasing to my eyes and more cohesive to the fantasy setting. It's sort of like how you can read a comic book, with superheroes dressed in all sorts of ridiculous costumes, and you overlook it because it just fits with the setting. Take those same superheroes and put them in a live action movie, and you start to realize how ridiculous those same costumes could look. That's why, I'm sure, that the X-Men ended up with single-color jumpsuits. My biggest problem with realistic graphics in MMOs is that the inconsistencies stick out like a sore thumb. I know what real people and places look like, and I can form a pretty detailed mental image of what a fantasy element should really look like if it existed in the real world, and some things in games that attempt a realistic look fall flat. 

Really, though, it depends on the setting. If it's a modern day MMO set in a close approximation of the real world, where tech replaces magic, realistic graphics would fit well. In fantasy, I'd rather it be more cartoonish, because the very nature of a cartoony look allows the artists to be more free and wild to come up with outrageous things that are perfectly believable within the context of the world.

I've always wondered why I try to play MMOs that are more in keeping with what I want gameplaywise, such as Vanguard, but I always gravitate back to WoW. WoW's gameplay is nowhere near my ideal MMO, but I feel... well, for lack of a better word, more comfortable with it. I think the graphics have as much to do with that as anything else, and probably moreso.

Hard to select really. To me, "asian" divides up very roughly into:

1) Cutesy anime - which i can't handle at all, but then i assume it's aimed at kids.

2) Anime - this looks good but the male characters in the games are all too metrosexual for me.

3) Realistic-anime blends - more like Lineage. I think that style is pretty cool.

I also think the western style follows a similar pattern where there's a sprectrum from cartoony to realistic with cartoony-realistic blends in between something like WoW -> Lotro -> EQ2 -> WAR/Vanguard/AoC/DaoC.

In theory i'd go for realistic but usually what that actually means is very dark and very dull, so in practise i'd go for something that was maybe 2/3 realistic and 1/3 cartoony (either western or asian cartoony).

As others have said though, if a game had my favourite graphical style but it didn't run really smooth then i'd go with a game that ran smooth instead. I think that pulls it back to more of a 50/50 cartoony-realistic blend.

I prefer 1D graphics and people with really big heads.

Of all the ones available right now I would go with the artistic style of WoW.. But I would like to see a mix of artistic and realistic that uses a high poly count but in an artistic world.

Flame me if must but, a mix of Warhammer online and Age of conan would be perfect IMO

I'd say Asian, mainly because realistic is really not that realistic.  Most developer that make realistic graphics put too much focus on realism and forgot to polish gameplay.  Gameplay should always come first before graphics in both quality and design.

I'd play a MMORPG even if it is 2D or Cartoonish if the gameplay is solid and entertaining, good graphic quality and interesting graphic design is always a plus though.

Something just outside of realistic is good enough to satisfy me.  I found the graphics in World of Warcraft to be a bit too cartoony for my own personal tastes.  Age of Conan had potential as far as realism, but was poorly implemented, in my humble opinion.  I think Lord of the Rings Online did a decent job with balancing realism/cartoon like graphics.  If there's plenty of eye-candy and the game isn't flat-out ugly on all fronts, then I'll usually go for it.

I hate too realistic graphics like in AoC. I like the game to be realistic yet beautiful looking. 

The characters must look as real as possible (not 'ugly' though, like models instead). Not overdone either, so they shouldn't look like heroes or anything. Normal people.

Clearly realistic, lush and detailled like the world of AoC or LOTRO. In terms of characters also realistic, but also sorta fashionable. I dont want only dull gear like in EQ2. I want  my char to look unique and cool.

While graphics don't make a big difference to me, I want to see more realistic styled graphics on any game I play.  You can certainly get some of the asian games that I would say have realistic graphics, as opposed to hyper-stylized, and so some of those games would also fit into the "realistic" mold.

Anything is fine as long as there isn't >9000 Vegeta hairstyles running around...

Which leads to the argument graphics < gameplay.

 I like realistic graphics, but came to conclusion that REALISTIC, FLUID ANIMATION is more important to me than character models. I can't stand jerky/unnatural movement of my avatar in any game. These days motion capturing isn't too expensive so I can't "forgive" developers sloppiness in that area.