The Wonders as Captain Geech and the Shrimp Shack Shooters in That Thing You Do!. 
(OK, so that’s a fictional band playing a fictional band…)
The Louisiana Gator Boys from “Blues Brothers 2000”? B.B. King’s name in that movie was Malvern Gasperon.
I have that soundtrack and that’s some good stuff on there, even if it is supposed to be parody/homage.
Heck, The Wonders were so popular that one of their songs was covered by a different fictional band in “My Big Fat Greek Wedding.” 
I think Alice was also in Dark Shadows.
Declan
The Circle Jerks were in the movie Repo Man.
A wonderful film which has been released on dvd finally. Remastered to boot, and Neil may have re-edited it, too.
Lemmy Kilmister was “The editor of the school magazine” in Airheads.
In the climactic scene of To Sir, with Love (1967) one of Sidney Poitier’s students gets up and sings the title song to him. That singer was the real pop singer Lulu; the backing band were the real band The Mindbenders.
He also appeared in Hardware, as a water taxi driver who happened to be a big fan of “Ace of Spades”. 
If solo performer counts, there are about 30 movies in which some random dude gets up and sings a song and it’s actually Elvis Presley.
When the Indigo Girls were at the height of their popularity, they played a bar band-- or part of a bar band, I don 't remember which, they may have just been the lead vocalists and guitarists of a five person band-- in Boys on the Side. They even had a couple of lines.
The Red Elvises were featured quite a bit in, “Six-String Samurai.”
Also, Tito and Tarantula were featured during the snake dance in, “From Dusk 'til Dawn.”
Slightly NSFW
<div class="lazyYT" data-youtube-id="Hk0tHeotroA" data-width="480" data-height="270" data-parameters="feature=oembed&wmode=opaque"></div>
Reel Big Fish perform in Baseketball.
Doesn’t count but blink-182 are in American pie whilst “Mutt” plays in the background.
Hair band Vixen performed in the sex comedy Hardbodies as the band “Diaper Rash.”
I was going to say that the Red Hot Chili Peppers were in Point Break but now that I think of it it may have only been Anthony Kiedis. Who didn’t sing.
On a slightly different note, “opera star” Kathleen Jenkins and actual opera star Bryn Terfel appeared in the BBC production of Under Milk Wood as Polly Garter and Rev Eli Jenkins respectively; both sang.
What a great, unexpected scene in a great movie…for those who haven’t seen the clip, check it out.
I believe the The Plimsouls’ name wasn’t mentioned as the bar band in 1983’s “Valley Girl” - Nicolas Cage’s career zenith :D.
I only vaguely recall this, but in the 1988 “Dirty Harry” movie The Dead Pool, a rock star (played by a pre-fame Jim Carrey) is killed, and Guns & Roses appear at the funeral. I’m pretty sure they were supposed to be other rock stars, but not themselves. They don’t play, though, they’re just there.
White Lion was in ‘The Money Pit’.
Peter Frampton and The Bee Gees joined forces as Sgt. Pepper’s Lonely Hearts Club Band in the dreadful, and yet awesome, film of the same name. Aerosmith also appears as The Future Villain Band.
There are probably a few others that could be included from that movie but that’s all I got off the top of my head.
The Strawberry Alarm Clock in Beyond the Valley of the Dolls