Through a Glass Darkly discusses one of the not-so-pretty situations in gaming:
People living through their characters.
While his discussion mostly focuses on those few who seem to express the poison and vitriol of their lives through their characterizations (which, as Strike Team Charon points out, is a fair catharsis), I consider it a fairly strong warning sign about crossing the lines between fantasy and reality.
"What do you consider insane?"
"The inability to determine the difference between fantasy and reality."
"Are you sane?"
"I'm sane enough to know I can't make that determination."
That's not to say that it hasn't been done, and that it hasn't been done well in my life. There are moments I have lived through my game, if not so much through my characters. At one point, there was a situation where I (inadvertantly, as GM) made the LintKing's character, Unakai (whom, if he blogged, he could tell you much more about) very unhappy and it was miserable for both of us, despite his and Unakai's obvious differences.
Notice that I'm primarily a GM: if anything, it is my games that define me. You can find echoes of me in some of my characters, but it is the worlds I create that would more likely give you insight, rather than the individuals.
I started considering it (probably somewhat cynically) this morning, in regards to what my characters express about me. Jinx-Jobina might express my feelings of frustration in trying to express what I synthesize of the world, only using a language that has not only a verbal and somatic requirement, but gestures that need four arms and hands to really get out "right." Maybe Trahern represents my tragedy of having my "sight" stripped from me. As for Damascus, she's the only character name Our Sweetie ever tends to use for me. And sometimes it's very true: I'll leave the subtlety to others and bash my way through things.
(There are a couple of people who know me as my Fiona. With her, it's fairly obvious that she's reflecting my taking a moral high road that while it has its rewards, will eventually end up destroying my emotional needs. [snort])
Realistically, however, I don't think of myself as my characters. There are some who have paralleled me fairly closely at times, but maybe that's the real difference as to why I don't think of myself as a player: I will act as the puppeteer, but I will not give the final breath of life to my character creations.