Is it just me, or are female bassists almost always smoking hot?
I assume the OP meant to exclude women who only sang backup, since there are tons and tons of those, from solo artists like Sting or whoever who had the standard three women adding backup for a few songs, to the Grateful Dead when the then-keyboardist’s wife would add usually horrible back-up vocals.
Anyway, I’ll add Donna the Buffalo (a man and woman swap singing lead, but another woman plays keyboard; I think this meets the spirit of the OP. Besides the singing woman plays fiddle and accordion, so at least half the time she qualifies too).
Alison Krause with Union Station comes close the OP: she sings lead on most songs, but there are plenty of songs where someone else is singing lead and she just fiddles (she was first known as a fiddle player, so this is not the equivalent of playing tambourine).
Well, Talking Heads were mentioned in post #2. I guess Tom Tom Club meets the OP?
Superchunk
Titus Andronicus
Okkervil River
Lemonheads (circa It’s a Shame About Ray)
Low (although Mimi Parker shares lead vocals)
The Decemberists
Of Montreal
The Minders
How about Mrs. Fiend in Alien Sex Fiend?
Oh yeah. For the record, I didn’t count Low because Mimi Parker sings a lot, and sings lead on a couple of songs.
Jens Lekman usually tours with an all-girl backup band, does that count?
This. The woman has outshone everyone else in the band each time I’ve seen them. She’s incredible.
Christie McVie certainly deserves a spot in this discussion.
Now she has two! 
Shirley Temple’s daughter, Lori Black, played bass on a few Melvins albums in the late 80s and early 90s.
The Japanese noise metal band Boris have a female guitarist named Wata, who may be the reincarnation of Jimi Hendrix. She takes vocal duties occasionally (and sang on most of their recent techno album “Attention Please”) but is mostly known as a guitar player.
Gonna give some caveats to that one:
All That Remains is a hard rock/heavy metal band that has a girl in it. You can see her in the helicopter in the beginning of the song. Also take note how hard the song is. She sings barely…but it’s mostly screaming
The aforementioned Sick Puppies has a female bassist. This is one of their harder songs but they do also have some more “chill” rock songs.
Skillet is a rock band that has TWO girls in their band. Rythim guitar and drummer. The drummer girl sings pretty often, but I still think it counts cuz I mostly want to put in some of my favorite heavy bands.
Don’t forget Halestorm and Flyleaf…they don’t really fit the OP cuz the girls sing…but I love them.
I really dig Halestorm! That’s my kind of vocals… not some light, ethereal voice, but one with some real oomph behind it. I play Halestorm on my online radio show Metallic Blue (as can be heard here).
Rock on.
For a good period of time, Cracker had Brandy Wood on bass. Wikipedia says 2000-2004, but I could have sworn I saw her play with them after 2004.
However, it was some dude when I saw them last month.
Hear, Hear. I just saw ZPZ again last week and I agree. An amazing talent. What blew me away was, after watching her do all the sax, clarinet, flute, etc., she then DOUBLED the ultra-high-speed vibes part from St. Alfonzo’s Pancake Breakfast on synthesizer.
That would be a pretty cool piece of memorabilia, if you were into the band. Who wouldn’t want a piece of Jimi’s burnt guitar from Monterey Pop?
I guess that the Mamas and the Papas kinda count, because even though they all sang (and were equally male/female), I don’t believe Michelle Phillips much, if ever, sang lead. And she did play tambourine sometimes.
Jefferson Airplane- although Grace Slick was a lead singer, on songs with other lead singers she sometimes played piano, etc.
Kathy Foster, bassist and sometime drummer of The Thermals.
I didn’t see Fair Game mentioned. Fair Game was a group with Ron Keel on lead vocals and he had four, count them, four women as the backing band. The women played guitars (Tina Listo, Eva Marie), bass (Janna James), and drums (Stephanie Leigh).