Dye your hair, and you too can be a superhero!

*switches gears* The traditional style of anime doesn't leave much room for distinguishing characteristics. Given that all faces are drawn more or less the same way in a given show (and often across shows), that choices in clothing may be limited by considerations like uniforms, and that anime faces are generally blank outside of the eyes, nose, and mouth, eye and hair color (and hair style) are some of the very few ways in which a character's individual personality can be portrayed in a design. (It might or might not be relevant to point out that this is often true in Japanese society as well, where dress codes at school and work limit the opportunities for self-expression through physical appearance.) As a result of this, there seem to be certain conventions dictating how a character's eye and hair color reflect his/her personality. (As a side note, the smoothness of most anime faces makes distinguishing marks stand out that much more; for instance, the freckle below his left(?) eye is a huge factor in making Vash the Stampede's appearance so distinctive and memorable.) Through a considerable amount of "research", I've come to some hypotheses on the relation between personality traits and particular hair colors. Believe them at your own risk. (Also note: many of these theories are heavily influenced by Evangelion. I think this is reasonable, since much of anime is also heavily influenced by Evangelion.)

brown: Somewhat surprisingly, brown seems to be the default color for ordinary Japanese people in anime. Even in movies like "My Neighbor Totoro", where character designs are fairly realistic, half of Satsuki's classmates have brown hair. Because of this, a main character will almost never have brown hair, unless he/she is meant to be an everyday person (caught up in events beyond his/her understanding, most likely).

blond: Blond characters tend to be cheerful and flippant, and often not too smart. They're usually class clowns or sidekicks. Of course, blond is also the default Western hair color in anime; I don't think these two are related, though I could be wrong.

red: Similar to the Western stereotype, red-haired characters tend to be energetic, outgoing, and quick to anger. (See Asuka.) This is only true of bright red or red-orange, though; crimson-haired characters are more likely to be serious, even grim.

black: Black is, to make a vast generalization, the Japanese hair color, and black-haired characters tend to hold to traditional Japanese values; they're usually serious and diligent. Drawing a character with long black hair is one of the quickest ways to indicate beauty (especially when the art style makes *everyone* look pretty).

blue: Oddly enough, dark blue seems to be considered a pretty normal color, like black and brown. I really have no idea of where this came from, but as far as I've seen blue-haired characters tend to fit into the "everyday guy" category. Of course, this doesn't extend to light blue, which is largely confined to hyperactive, silly people and Ayanami Rei knockoffs (no offense intended, some of my favorite anime characters are Ayanami Rei knockoffs).

pink: As in the West, pink is a very feminine color in anime, and pink-haired characters are almost uniformly girlish and naive. There are very few assertive characters with pink hair out there, and when it's done it's usually intentionally reversing the stereotype.

white/grey/silver: White-haired characters are usually serene, otherworldly, and mysterious. (See Kaworu.) It's pretty rare to have a white-haired main character, since a main character is expected to be more emotionally dynamic. Of course, this only applies to young characters with white hair; on elderly characters, I don't think it means anything in particular.

That's all I've come up with so far, but I think it's pretty interesting, and holds surprisingly often. Please post with questions, comments, or counter-examples; after all, this is science! Well, social science. Maybe. Not that I know anything about social science.