Straight from my eventual post on the matter:
How does your character define themself? What part of their identity is most important to their personality and self-presentation?
In meatspace, we have so many affiliations, it's anyone's guess whether we consider ourselves a tuba player first, or a student, a Gators fan, a New Yorker, a mother, a nerd, a liberal. Our identities are comprised of so many different aspects of life that it's hard to tell which parts different people will choose to define themselves.
In game, there are less game-related ways to identify.
You can identify as:
your class - your spec
your race - a particular subgroup (Mag'har, Wildhammer)
your faction - a faction other than Horde/Alliance
Disclaimer: I don't typically read other posts on these topics prior to writing my own opinions! So if the topic seems a bit off of it's original intent, my apologies.
While I think Akabeko had a bit more of a role playing angle in mind for this shared topic, I'm going to take a touch more personal approach to it. Think of it as a "meatbag meets pixelself" type of fusion post, and by that I mean I'm going to tackle this from the view point of a non-RP player. Sure even us non-role playing types will be identified as "that one enhancement shaman" or "that one affliction lock" or what have you, and naturally we identify to some extent with our faction (insert "FOR THE HORDE" or "FOR THE ALLIANCE" here), but often we don't bother affiliating with our races. We non-RP types tend to choose races based either stats or pure looks, rarely do we know the histories and personalities behind the races that we play, unless we happen to pick up the information over the years.
Regardless of play style though - be it RP, PvP, PvE, RPPvP, or whatever other variation there may be - all players have something in common. All players will 1) project some sort of personality when interacting with others, be this their own personality or one they had in mind for a specific story/character 2) choose to either identify with a certain guild/clan that shares a likeness in thought processes to themselves or will fill the lone wolf type role. Naturally there are all sorts of shades and variations in what you may find a player identifying themselves as, but this is the general concept that I've gathered thus far.
The fine little details though are what make a character and player one. Like Aka stated, in the real world we often identify with being the bass player, the Packer fan, the couch potato, the reader, but how about in game? For me personally, on my shaman at least, I have always seemed to gravitate towards guild mom, raid leader, the negotiator between two butting heads, the soother, the stubborn "bitch", that one dead shaman on the floor. I've always tried (keyword) to be rational and to take care of my people. I've always tried to make sure folks were happy and tried to do right by my guild. These days though? I'm the bum who spends her time farming for mounts for an obscene number of hours at a time. I started my item hoarding long ago, but the habit seems to have exploded ten fold since my departure from the official raiding scene. I'm the lost girl in between guild homes, who even though finds this frustrating and lonely at times, is quite happy to have her little crew just a chat channel away. /join [channel name] is pretty much one of the best things ever.
Now, while I say "Oh, I don't RP" I do believe I have a bit of RPer in my blood. We've been over this a few times here at WoS already I think. I don't really have a huge story line for my shaman like I am beginning to develop for my druid, but she has been a huge part of my life for the past four years or so. Because of this she fits like a glove. She is the more confident me, the me that I was many moons ago. Her and I have been through a lot of good times and bad together, and she's very much become my online identity. That icon that I use everywhere? Yup, Saz at level 80 in Naxx 25 gear. Heck, I think I even had a picture of Saz for my Facebook page for a while (no you may not have a link!). But it isn't just I who identifies with my Saz personality, but it's my WoW friends as well. A friend of mine has dropped a few good lines that I'd like to quote "Every time I see a shaman, I do a double take and think it's you." and "Well, now I have to get used to your real face. Every time I think of you I see your shaman in my head." Kind of funny to think about how much her and i have become one in the same, or nearly so. I project myself through my pixel form, my pixel form represents who I am or who I'd more or less prefer to be. Well, maybe minus the horn and hooves, though those may be fun change.
To get back to the original question about how Saz defines herself. Essentially she and I identify as one in the same. We are aggressive when need be, protectors of our packs, we like to heal the wounds of our friends, and remove our foes from our paths. She may be a dark skinned alien with horns and I may be a pale ginger with glasses, but personality wise we are not so different. We are friendly to those whom are deserving, will ignore those who are not. We are fiercely loyal to those who show loyalty in return, though we are quick to sever ties if we feel we have been abused in some way. Always observing, always listening.
Shamans are spiritual visionaries of tribes and clans. These gifted warriors who can see into the world of spirits and communicate with creatures invisible to eyes of normal beings. They are beset by visions of the future and use their sight to guide their people through troubled times. Although the shaman may seem wise and serene at first glance, he is a formidable foe; when angered, his wrath is as fierce as those who have a connection to Eternals or nature. WoWWiki
Of course the entry doesn't even begin to cover my association with my various of alts, for yes, they all do have a somewhat individual personality, though they all do very much have an infusion of myself. If you'd like to read more about the personalities of my alts, their associations with each other, and to try to get a gleam of my personality showing through them, take a gander at this previous shared topic, Behind the Faces.