I love a strong female protagonist. I like them to be snarky, confident, and outgoing. The word vivacious comes to mind. I like it when their fault is they are irrational, I think it makes it easier to write about and leads characters down unexpected paths.
Pet Peeve in female characters - the "I don't think I am pretty" fault or the "I don't know why he is with me" fault. I want to ask them "Didn't your parents, guardians, grandparents, anyone tell you were pretty when you were little?" and come one girls know how to size each other up.
But what about you? What do you like in a female character? Even though I stated my Pet Peeve you may like that in the character. I am very curious as to why you do.