For me, it's their personality and story. Something deep and interesting. Distinctive look also helps. For example, Vivi from FF IX. I've been to Distant worlds concert in Sydney opera house recently (my fiance is big FF fan). When they were performing Vamo' Alla Flemenco, Vivi's appearance really caught my eyes. From there on, I looked up his story on wiki and such, it was really sad and interesting. Now I'm trying to find a copy of FF IX to play :X

Other examples are from BG2; Anomen is classic example for me