I could go for that. Shumer’s stuff seems more subversive and deeper than Louis CK’s … or anyone else’s.
Hey, 12-step, The Time sucked! 
Is there a special or something I can watch that shows off her best work? I don’t remember having near that reaction at anything I’ve seen from Shumer, but I could definitely be missing something.
Her best work is in her tv series. It’s brilliant.
Chelsea Peretti (Gina from Brooklyn-99) is a pretty hilarious stand-up.
Her SNL monologue was pretty good.
This one’s just funny. Dirty and oh, so funny.
Historical reality meets romance fantasies
Faux-personal relationships that are commercial
I didn’t link to any of her standup routines because they are not divided up by topic and are generally 30-60 minutes long and I don’t have the kind of time it takes to sort them out. Watch 'em yourself.
Never head of her until I saw her on Big Fat Quiz. She more than held her own.
Maybe in 1992. Not today.
That’s kinda what I thought. I used to enjoy Elayne Boosler’s stuff, also Laura Kightlinger and Rita Rudner, but that was a couple of decades ago.
The last four listed are not only my favorite female comedians, they are most of my top favorite comedians.
Amy Schumer I have not been able to understand as funny. I just don’t get it. She reminds me or Carlos Mencia. Maybe her sketch stuff is funnier, I’ll have to check it out!
Iliza Schlesinger, I’ll have to look into again. I watched about fifteen minutes of her special War Paint, and it seemed, well, redneck. It seemed like a little bit more sophisticated version of Jeff Foxworthy. Did I just see the wrong fifteen minutes?
It’s not very intellectual—mostly guys and gals and dating—but it’s very well done.
Ahhhhh… that’s probably just my snobbery coming out then. 
Ooo another one I’ve enjoyed is Chelsea Perreti.
I saw Paula Poundstone perform twice and I love her on Wait Wait Don’t Tell Me - I think she’s hilarious! I also love Kathleen Madigan.
Personally, I don’t think Amy Schumer is all that funny, but then I don’t like crude humor, and I find her very crude.
I love, love, love Poundstone on WWDTM. Heard her standup twice, on PHC, I thought she sucked both times. Her panelist duties on WWDTM are really her sweet spot. If I’m wrong (or missing something) please link me to her funniest stand up routine.
I saw Amy Schumer’s live show in Seattle last New Year’s Eve, and she was brilliant. She seamlessly worked into the act some disruptions from the audience, including a man who needed an ambulance.
Agree that the show is funny, but to nitpick the OP did specify stand-up comedy. If her stand-up is not as good (which I don’t think it is), then she doesn’t qualify as “best American female stand-up comedian”.
What’s Sandra Bernhard been up to? She is the greatest of all time for me. Don’t know if she’s current.
I saw Margret Cho, Amy Schumer and Lisa Lampanelli in a 6-month span last year. They were all drop-dead funny but Lisa was the one who most brought me to tears.
Amy is my girl tho. Love love love her TV show and her standup. But Lisa is the best of the 3 at standup IMHO.
Actually, now that people are mentioning it, Wanda Sykes is my all time favorite comedian.
My second favorite is another woman who plays mostly women’s and GBLT venues, named Kate Clinton; she is very sophisticated, never raunchy, and as political as Tina Fey with the personal touch of Paula Poundstone, my third favorite comedian.
My number four is Sarah Silverman.
You have to get down to six or seven before you start to hit John Mulaney and Patton Oswalt.