Lara Croft is probably the best known. Well, maybe other than Mrs Pacman. Or Sonia from Mortal Kombat.
My favourite have got to be Alyx Vance - that's a well-written strong female character. Edith Mossman is very plausible as well. Chell from Portal is fun to play, but her Dialog is kinda sparse - although the hilarious GlaDos makes up for it.
I really liked Faith in Mirror's Edge - especially the fact that her character could complete the game without ever killing anybody (the "test of faith" achievement) - which I felt was an interesting and original way to play a game very similar to an FPS.
I think the first female character I played was choosing the play the girl in Ant Attack on the spectrum way back when. Another memorable one was the hero(ine) of Saboteur II.
There's actually been a lot of good female characters in video games. Some are stylised in a sexy ways, but then again most of the guys look like greek gods with a decathon habit. So......