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Avatars don't really say much about a person's character to me, but they might reveal some kind of hobby or other interest. The only thing I really even use them for are identifying people I don't know very well.
I have a tendency to judge people based on their avatars. If it's from a popular anime (FMA, Inuyasha... you know, those shows), I usually immediately assume that the user sporting it is a complete idiot until proven otherwise. If it's an animal, the user sporting it is immediately branded a furry.