These sort of things discriminate against those of us who have no idea how to describe appearance! If only I could upload a photo and it would make a "closest match".
On another note, I went to make a pair of them for a friend and her husband's anniversary, but he has very little hair and there is no kind way to not put hair on something like this.
Maybe this could be a crowd sourceable feature. Someone on mechanical turk or crowdflower or 99 designs could take a photo and create your character and send the design back to you which you can print later.
I've seen those mall photo booths that supposedly do something like this - takes a snapshot of you and caricature-izes it. I can't for the life of me think of what they're called or who makes them.. Only other thing I remember is it's adorned with a picture of a girl who wearing a beret who looks like an artist.