My immediate response to this question was Elizabeth Bennet in Pride and Prejudice, for her quick wittedness, good sense and spirit, then Jo in Little Women because of her independence and intelligence and Cousin Helen in What Katy Did as she was such a good person. But these are all characters from books I read a long time ago; there must be some more modern female characters that I like.
It seems I like strong, determined women with a mind of their own and able to cope with difficult situations. So why is Elizabeth Bennet such a favourite, after all she didn't have to cope with serious illness, or live in poverty, or deal with manipulative, domineering, homicidal men, or make a home in the American west? I think maybe it's because I see her through rose-coloured glasses and because she is the first female character that caught my imagination when I first read Pride and Prejudice, possibly the first adult book I read.