When you say pop, do you mean modern pop or do would you include things like The Shangri-La's, the Supremes or the Ronnettes? Because they are all great classic pop and I would definately suggest getting a Phil Spector (he produced most of them) compilation. Their modern day equivalent would be the Pipettes (youtube "pull shapes").
Punk/alternative:
Patti Smith (the "Poet Lauriet of Punk")
Blondie
X-Ray Spex
Siouxsie and the Banshees
PJ Harvey
Liz Phair (Exile in Guyville only)
the Breeders (Kim Deal's, the Pixies bassist, band)
My Bloody Valentine
Folk:
Joanna Newsom (she plays the harp)
Joni Mitchell
Tracy Chapman
Laura Marling
Indie pop (not shitty, trust me):
Magnetic Fields (they alternate between male and female vocalists)
Tallulah Gosh/Heavenly (basically the same band, Jardin de Heavenly is definately worth checking out)
The Pipettes
Feist
The Vaselines (aka. Kurt Cobain's favourite songwriters)
Dirty Projectors (3 female singers, 1 male singer)
Florence + the Machine
Best Coast
Vivian Girls
Dum Dum Girls
Other:
Aretha Franklin
Bjork
Charlotte Gainsbourg (daughter of Serge Gainsbourg)