Cindy Blackman, actually.
No love for The Thermals? Kathy Foster is the bassist.
Poison Ivy was a founding member of The Cramps, but did not, as far as I know, sing.
To those who’ve mentioned The White Stripes: Meg has sung backup on some songs, and even taken lead on a few, such as “In the Cold, Cold Night” from the album Elephant.
Gillian Gilbert, of New Order. I think she did do some singing, like most band members do, but she was never the lead vocalist.
Robert Palmer? 
Trip Shakespeare: Drummer Elaine Harris was the only one of the four members who did not sing.
Shonna Tucker of the Drive By Truckers. Although she looks kinda like a dude.
Somebody mentioned Pat Smear, which got me thinking…
Donna Rhia and Belinda Carlisle drummed for The Germs, but I don’t think either of them ever did vocals for the band, did they?
I think he meant Robert Palmer.
Sara Lee played bass for Robert Fripp’s League of Gentlemen and later for the Gang of 4.
Lynn Perko was the drummer for the Dicks and Sister Double Happiness.
Poisen Ivy for the Cramps was mentioned earlier and she only plays bass.
Lordi’s keyboard player is a female character and most likely played by a woman.
[trivia]The cello lady is Melora Creager, singer for Rasputina.[/trivia]
She did backing vocals during their live shows, but I don’t think she did any in the studio recordings.
Chrome (during the period when Helios Creed rebooted it and was on Cleopatra Records) had Z Sylver on keyboards.
Do “session” players count? Jody Linscott has been in many bands. I don’t believe I’ve ever heard her voice.
Mellencamp ALSO featured Susan Voelz on violin for a time. She was a member of Poi Dog Pondering.
CH
I don’t believe Rosie Stone of Sly and the Family Stone did vocals (Cynthia Robinson, the trumpet player, did occasionally sing).
How about non-singing members of bands with a female vocalist? Do they count?
Coal Chamber has had two female bassists. The first was Rayna Foss-Rose and the second was Nadja Peulen
Skid Row- Rachel Bolan on bass.
I’m thinking just about every other alternative band in the 90s stretching into the 00s that had female bass players.