I personally do not care. I just want a character (assuming we meant games without character creation) to be easily different and unique from others. Very often some games used the same type of beauty in their characters which have gotten stale over time. If it means to have an ugly character, then I am fine by that. I just do not want to be guessing the characters appearance the third time around when being asked.
EDIT
I just forgot to add that I prefer a character personality over their appearance. I will take an ugly character with charming personality over an attractive person with a wooden personality.
EDIT
I just forgot to add that I prefer a character personality over their appearance. I will take an ugly character with charming personality over an attractive person with a wooden personality.