Teresa of the Faint Smile from Claymore doesn't have any memorable quotes but I love every single word she spoke.
I can't think of many characters but if I had to pick a female character with the best quotes it'd be Watanabe Saki from Shinsekai Yori/From the New World.
If you would've asked for a male character I'd definitely say Itachi.
Edit: Crap I thought the question was ''What is your favourite quote from a female anime character''
Anyway, my favourite female anime character is Nagisa Furakawa/Okazaki.
This is my favourite quote from her.
''Meeting you was the best thing that ever happened to me.
You made me so happy, I don’t want you to be lost or afraid or anything like that.
From here on out, I know things might be hard sometimes, but no matter what, please don’t ever regret the time we spent together.''