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Examples of GOOD movies with strong female leads?

So with the recent release of Sex and the City 2 I got into a little debate with my girlfriend about female leads in movies. She thinks that any movie with a strong female lead is going to be disliked by most men because it makes us feel intimidated, and I argued that it's only because most of the BS "strong leads" out there are actually just major b!tches, and that she is just going to automatically like any movie featuring a woman because it is so rare, regardless of how big of a POS it is.
Now, I really like a well done female lead, but my gripe is that in most of these films the "strong" woman is actually just a woman who has been reduced to what I would consider negative stereotypes; obsessed with shopping, crying and making a fuss out of a truly mundane set of problems when they have SO much to be grateful for, and ultimately falling back on a man to solve there problems - even if only in a veiled way.
To me, a strong female lead would be someone more like Sigourney Weaver in Alien, Uma Thurman in Kill Bill, Gabourey Sidibe from Precious, etc. etc. A woman who has a real set of problems and deals with them in a real way (whether that solution is morally justifiable can be arguable), potentially while leading a group of other people.
Unfortunately, the above three were the only ones I could come up with off the top of my head, which makes it seem like the only place a woman can be strong is an action film.
My girlfriend says that any movies with female leads are going to be doomed by a sexist, male-dominated group of critics, and I say that most good female leads are doomed by the sexist, male-dominated groups of executives in the movie studios who will rarely actually produce a movie with female lead that would work, and the critics are just doing their job to fairly review an unfair set of films.

So... what are some good movies with strong female leads where the main character is ACTUALLY strong, a leader (or at the very least independent), and female? I would appreciate films of any genre.
Also, if you're feeling like typing out everything, what are YOUR thoughts on strong female leads in Hollywood and movies like Sex and the City 2? I'm definitely going to read all the answers so don't feel stupid if you wish to type a lot.