I’d like to put this out there - these bands have another thing in common, female lead singers. I always hate when a trivia question has more than one correct answer, so if you pick one of the many good suggestions with a male singer you’re good to go.
Plus, they’ve never been in Cliff Clavin’s kitchen.
Pretenders
beastie boys
Stray Cats
Nine Inch Nails
Dead Kennedys
Eels
REM
Pulp
Throwing Muses
Squeeze
Belly
Rush
Cocteau Twins
Somebody actually says “The REM”?
Oh, and I’d add Butthole Surfers.
About as often as they say The Rush.
True. Ramones would be an example that actually fits. 
Models. Probably not well known outside Australia, though.
Delays, also probably equally unknown outside the UK.
Ramones.
ETA: Just saw it was mentioned.
The The. Few are aware that they’re actually just “The”.
(Kidding!)
Indigo Girls.
Gotcha covered in my first reply; was a little too clever for my own good
My bad! I’ll beat you to it next time around 
I always referred to them as the The The.
Guess Who!
Who?
Yes!
Them?
Wham!
If anyone cares, I went with:
What do the following have in common?
The Backstreet Boys
The Dixie Chicks
The Eurythmics
The Grateful Dead
The Talking Heads
Smashing Pumpkins
[spoiler]None of them are actually the names of bands. The groups you’re thinking of are:
Dixie Chicks
Eurythmics
Grateful Dead
Talking Heads
The Smashing Pumpkins[/spoiler]
I really like this question — I think it’s my favorite that I’ve put up so far.
To ptr2void and Shoeless, Exapno Mapcase, Jenova Tokka, and everyone else who pitched in — thank you.
Scorpions fits as well. Annoys me to see The Scorpions.