One of the more unusual traits of Anime and Manga is the varied and often unnatural hair colors. While the trend was probably introduced one day by a bored colorist, it's taken on an casual symbolism of its own, informed by the culture it developed in. While I think the symbolism is still fairly consistent, there are certainly no hard rules to this, so take my interpretations with grain of salt.
Here is a basic summary of what I've learned from browsing the web, conversations with other fans, and by own brief stint watching anime:
Black: Neutral. generally positive connotations -- keep in mind that this is the normal hair color in Japan; all other hair colors are "unnatural" in that culture, and consequently somewhat suspicious.
Blonde: This hair color has two diametrically opposite interpretations, although which one applies in a particular case should be relatively clear.
in either case, blonde-haired characters usually mean trouble.
- obvious power and intelligence. often calculating and self-serving.
- ditzy and immature. accident-prone.
Brown: Nothing screams "I'm a stock character" like having brown hair. there are of course exceptions.
Red: In women, red hair generally connotes a brazen, confident character -- often having special abilities. male characters with red hair tend to be quiet and humble, but skilled fighters.
Grey: Grey hair usually connotes a character with a hidden power that will be revealed later in the series. these characters are usually very intelligent and often (although not always) evil.
White: On younger characters, full, white hair gives a sense of dignity and style. on older characters, it may just mean they're ... well, old.
Blue: Likable characters. shy, sweet, smart, funny. one notable exception is the Kento of Samurai Troopers (sometimes translated Ronin Warriors), who is the exact opposite. Rei from Neon Genesis Evangelion might be another example. She's shy, but at least outwardly doesn't display most of the other characteristics.
Green: These characters are usually good at heart, but misguided. Seen in an antagonist, it often means the character will defect to the side of the "good guys" by the end of the series. Sympathetic characters (good guys) tend to be rogue-ish but goodhearted.
Mononoke Hime didn't really divide most of the characters into a "good guys" and "bad guys" (with some exceptions), but I think this interpretation can still be applied to San in an oblique sense.
Pink: Generally only seen in female characters, girls with pink hair are cheerfully cute, often to the point of being downright obnoxious (as if you needed hair color to pick up on that).
Purple: Your guess is as good as mine; there just aren't that many examples to work from. characters tend to be upbeat, but other than that, it's hard to generalize.
Do you have something to add here? Do you disagree, or have counterexamples? (Am I full of crap? ^^