I'd be in favor of anything that aids in communication.
If the avatar were strictly someone's head shot, (a big if, I know) then I would be able to know something about the person. For example, I'd be more willing to trust the advice of someone who looks like he (or she) has been around the block a few times, than someone who looks like he is skipping school.
Sometimes someone will put in their sig... "Ford Technician for 30 years"... I'm more willing to accept their comment.
If the avatar is a young woman who appears to be trying out for the SI swimsuit edition, then it's distracting. (Even though I like that as much as the next guy.) Unless you really are that person, in which case see the point above.
Closely related are the little smiley pictures. Think about it... those things communicate "emotion", which really is very important to communication. The same words might have very different meanings when they are accompanied by the emoticons.