Yeah, what Jim said. Personally, I look about 23 without a beard and about 33 with one. Definitely best to look older imo.
I think a lot of guys look much better with facial hair. Here are some before and after pics I found that illustrate what I mean..
The Beard Contest 2007 - Rob The Beard Contest 2007 - Jeremy The Beard Contest 2007 - Josh
As far as women, they might equate having a beard to a guy having a more laid back, artsy job, by extension making him more fun to be around. Or they might think that he is a woodsman / outdoorsman, making him more knowledgeable / handy / attractive.