Gameplay
Graphics
Connection
I have to have a connection to my character. I have to feel it. I have to like it. But having a connection with a character is based off another set of criteria.

Hey Ma, I'm Pretty!
So, how does one feel connected from the get go? Simple, with the ability to create their own avatar! People have different tastes of course, and personally, I like my avatar to be a humanoid, I of course want my avatar to look cool, and have just a touch of me, regardless if my avatar is male or female.

However, most games don't allow this key feature to it's fullest extent. Granted, MMOs have evolved from the old days of Diablo-inspired Korean isomatric MMORPGs, where a character's look and even gender is based on the class. However in most games, I get to choose from a bunch of pre-selected faces, hairs and skin tones, with little else other then equipment to stand out from the rest of the virtual world.

I can only hope that more games would come up with more innovative features for customization! Morphing, while technically challanging, seems like a good way to go in my book. Nothing brings more joy to me then being in a sea of different faces, like in Second Life, where everyone has his or her own definition of looking good or just unique.

Second Life Clarification: Wear a dick costume is not considered being unique, to me. Thankfully, it has not happened much.

MOAR SHINIES!
Items are the next thing that allows one to be unique. However, apart from Star Wars Galaxies (Before they made an overhaul of the game, called NGE), no other game has allowed one to be truely unique.

There were some innovative ideas that allowed one to wear what they like while having the stats that come with others, like the "Appearance Paperdoll" that is seperate from the basic one. I want to see people wear what they want to wear, not what they are forced to due to some numbers!

A more modular apparel system would be much welcomed as well. I believe most who have played MMOs can relate to the fashion disaster syndrome, which is, specifically, totally mismatched armor pieces that just don't fit each other, as well as colors that even the blind can see and hate.

I has M4D Sk1LLz!
Other then looks, the one thing that defines a character is it's gameplay aspect; the skills of the character. If I play a warrior for example, I imagine a fearsome hulking veteran of many wars with a huge big ass sword swing it around in big arcs, clearing a path through the field of enemies in front of him. I can't do that if most games have the warrior as a shield bearing pansy who taunts a target before prompty hiding behind his shield, so that his team mates can attack, while stomping the ground in a fit of dispair that he can't do much else.