Yes. “Pop Goes the World” which I’ve been trying to find to buy for a reasonable price.
They’re from Santa Barbara. Glen Phillips still plays around town. The name comes from some Monty Python reference that I don’t particularly remember.
I wanted to mention Dexy’s Midnight Runners’ “Come On Eileen”.
When I go to find songs, I’m often amazed by the other songs by the guy I was looking for one song from. I think anyone over 30 would recognize all of these songs, but the bands have been all but forgotten.
Alan Parsons Project - Don’t Answer Me, Time, Eye In The Sky, Where Do We Go From Here
Ambrosia - Baby Come Back, How Long Has This Been Going On, That’s How Much I Feel, You’re The Only Woman, You’re The Biggest Part of Me
Billy Squier - My Kinda Lover, You Know What I Like, Everybody Wants You, Rock Me Tonight, In The Dark, Emotions in Motion, The Stroke
Jerry Reed - East Bound and Down (from Smokey and the Bandit), Guitar Man, She Got the Gold Mine (I Got the Shaft)
Robbie Dupree - Hot Rod Hearts, Steal Away
Poco - Crazy Love, Heart of the Night, Call It Love
XTC - Making Plans for Nigel, Generals and Majors, Dear God, Senses Working Overtime
Warren Zevon. He had a fantastic career with a whole catalog of great songs, but to most people, his career begins and ends with “Werewolves of London”, and most people could name that song in the first two notes.
bearflag70 has the wrong songs for some of the bands 
Aztec Camera - Somewhere In My Heart
The Stranglers - Golden Brown
Godley & Creme - Under Your Thumb
A few other ones that I don’t think have been mentioned yet:
Wallflowers - ‘One Headlight’
Dishwalla - ‘Counting Blue Cars’
Meredith Brooks - ‘Bitch’
Kim Carnes - ‘Bette Davis Eyes’
Europe - ‘The Final Countdown’
Crash Test Dummies - “Mmmm Mmmm Mmmm Mmmm” and “The Superman Song.”
Or ‘Musical Friends’, ‘Goin’ to the Country’, ‘Burn, Baby, Burn’ and especially ‘Wonderin’ Where the Lions Are’… from the '70s.
Believe it or not, The Wallflowers actually had a ton of charting singles that I still hear today. Besides “One Headlight” there’s “6th Avenue Heartache”, “The Difference”, “Three Marlenas” and a cover of “Heroes”.
I’ll add “Tokyo” and “Coldest Night of the Year” to Bruce Cockburn’s list. Cockburn was pretty prolific in the last 70s and early 80s.
Dream Academy - Life in a Northern Town
Escape Club - Wild Wild West
Deee-Lite - Groove is in the Heart
The Fixx - Saved by Zero / Red Skies / Secret Separation / Stand or Fall / One Thing Leads to Another / Are We Ourselves
Jan Hammer - Miami Vice Theme
Harold Faltermeyer - Axel F.
Lipps, Inc. - Funkytown
The Vapors - Turning Japanese
Joey Scarbury - Believe It or Not
Bow Wow Wow - I Want Candy
Tony Basil - Mickey
Buckner & Garcia - Pac-Man Fever
Peter Schilling - Major Tom
Icicle Works - Whisper to a Scream
Timbuk 3 - The Future’s So Bright, I Gotta Wear Shades
When in Rome - The Promise
Thjis Van Leer; Jan Akkerman; Bert Ruiter; Pierre Van der Linden (from memory)
<looking at Focus III CD> no, misspelled Thijs. But I’m 51, not 47.
I wonder if the same age group would remember the song Sylvia? I remember hearing it a lot around the same time as “Hocus Pocus” although it obviously didn’t last as long in people’s memory.
If you want to hear something really special, try and find a copy of Jan Akkerman’s “Streetwalker”. Oh here! I found it. Streetwalker
Oh yeah, the OP. How 'bout
Jon Butcher - Wishes
Head East - Never Been Any Reason
Ozark Mountain Daredevils - Jackie Blue
Outlaws - Green Grass And High Tides
Sugarloaf - Green Eyed Lady (unrelated dancing girl video SFW)
Pure Prairie League - Amie
Michael Shrieve - Spellbinder (okay, this one doesn’t really fit. I just like it.)
How 'bout Steelers Wheel? I’m sure they’re big in Europe-- or were, I don’t know-- but here in the US their known for Stuck in the Middle With You. Some will probably know the Absolutely Fabulous theme song too. But not many.
“Smokin’ in the Boys Room” by Brownsville Station
“Locomotion” by Little Eva
“Na Na, Hey Hey, Kiss Him Goodboy” by Steam
“The Lion Sleeps Tonight” by the Tokens
“Take My Breath Away” by Berlin
“Play That Funky Music” by Wild Cherry
I’m old, I’d’ve known all of those.
Name this band: King of Wishful Thinking (best recognized from the soundtrack of Pretty Woman.
Go West
Name this band: Perfect Way.
Scritti Politi
Name this band, whose most well-known song, Baby Come Back, is featured in a bunch of new commercials these days
Player
Congratulations on blowing my mind.
This one is more for people familiar with memes, but…
Dragostea Din Tea or “Numa Numa” (or, if you’re really picky your Romanian, “nu ma nu ma”) is done by O-Zone,* who were actually quite a hit in Europe from what I understand, but most people here know them as… well, they’ve never heard of them but they CERTAINLY know “that song in a weird language that fat kid danced to.”
*Or Haiducii in Italian, but 99% of people heard the O-Zone version.
Ray Parker Jr. - “Ghostbusters”
Live - Despite having a lot of great songs, people only know them for “Lightning Crashes”
Joan Osborne - “One of Us”
Eagle Eye Cherry - “Save Tonight”
Blind Melon - “No Rain”
Norman Greenbaum - “Spirit in the Sky”
Mungo Jerry - “Summertime”
Hell yeah. This song plays at the very end of Napoleon Dynamite. That’s the first time I ever heard it, and now I love it.