The "Deep Down I Just Want A Mary Sue" Category
1. They code as "special" within the source text. This is hard to explain and easy to recognize.
2. An aura of mystery.
3. Formidable reputation.
The "Playing This Can Get Exhausting" Category
5. Immense capacity for rage.
6. Obsessive and/or particularly dogged determination.
7. Formidable willpower.
The "This Is Kind Of Unhealthy" Category
8. Trapped in the moment (or sometimes a whole era) of past trauma. You can usually tell if this is the case by looking for repeated flashbacks of the tiny version of the character looking traumatized.
9. Carries a burden of guilt, whether deserved or not.
10. Emotional sleight of hand: masks his true issues in some way, often by faking normal around much more obviously maladjusted people. May or may not actually believe the mask.
11. Presents a front to the world that is notably different from his inner self, whether deliberately (ideal) or unintentionally (can also sometimes qualify).
(This category is more likely than the others to attract also-rans.)
12. Dead by the end of their canon, even if it's retconned later. Characters who die and come back as was planned all along (I'm looking at you, John) don't count.
13. Self-sacrificing (although he may not necessarily die this way. Then again he might).
14. Self-destructive (although he may survive. Then again he might not).
15. Goes knowingly to his death.
16. Inescapably, unfixably tragic natures.
(Every single character I've fixated on slots into the above category in some way.)
The "I Don't Know Where Else To Put This" Category:
17. Mentor figure.
18. Bonus points: cool scars or a missing eye.
Assorted bonuses often applicable to non-fixated favorites and also-rans:
a) Father issues (often but not always specifically "craving their father's love and approval despite being constantly and royally screwed over by him").
b) Being a spy.
c) Survivor's guilt.
d) Obsessive unrequited love or devotion.
e) Identity issues (especially for female characters, but not always).
The only category that my current fixation is lacking in is the first one. He has a freaking bingo in some of the others.
When I play out Lockon (considering my cast on polychromatic and all my future plans, I hope it's not for a while), I will just link this post and ask for suggestions on acquiring a new character obsession. With these things I'm a serial monogamist.
Also, I have discovered that unless the character is really inappropriate for it, I can totally write porn about these guys despite my general aversion to writing porn with male characters in it. I wish I'd discovered this back when I was into Gundam SEED. Well, maybe someday I can get all nostalgic, rewatch, and write some Mwu/Murrue.