There's a bunch of names that immediately spring to my mind BUT I do not know for sure if it is because I heard them in 1980s and 1990s, before widespread internet.
A-Ha, "Take On Me"
Darude, "Sandstorm"
Trans-X, "Living On Video"
I'm doing a quick gander about some that tickle my memory...
"Video Killed the Radio Star" - The Buggles
"Funkytown" - Lipps Inc.
"99 Luftballons" - Nena
"Don't Worry, Be Happy" - Bobby McFerrin
"Achy Breaky Heart" - Billy Ray Cyrus
"Spaceman" – Babylon Zoo
"Mmm Mmm Mmm Mmm" – Crash Test Dummies
"Scatman (Ski-Ba-Bop-Ba-Dop-Bop)" – Scatman John
"Cotton Eye Joe" – Rednex
US list + others
Sheb Wooley – "The Purple People Eater"
Boots Randolph – "Yakety Sax"
Kyu Sakamoto – "Sukiyaki"
Napoleon XIV – "They're Coming to Take Me Away, Ha-Haaa!"
Caramba - "Hubba Hubba Zoot Zoot"
Don McLean – "American Pie"
Hot Butter – "Popcorn"
Carl Douglas – "Kung Fu Fighting"
The Boomtown Rats – "I Don't Like Mondays"
The Weather Girls – "It's Raining Men"
Frankie Goes to Hollywood – "Relax"
Harold Faltermeyer – "Axel F"
Baltimora – "Tarzan Boy"
Falco – "Rock Me Amadeus"
Comments
A-Ha, "Take On Me"
Darude, "Sandstorm"
Trans-X, "Living On Video"
But here's a nice list of some. https://en.wikipedia.org/wiki/One-hit_wonder
"Video Killed the Radio Star" - The Buggles
"Funkytown" - Lipps Inc.
"99 Luftballons" - Nena
"Don't Worry, Be Happy" - Bobby McFerrin
"Achy Breaky Heart" - Billy Ray Cyrus
"Spaceman" – Babylon Zoo
"Mmm Mmm Mmm Mmm" – Crash Test Dummies
"Cotton Eye Joe" – Rednex
US list + others
Sheb Wooley – "The Purple People Eater"
Boots Randolph – "Yakety Sax"
Kyu Sakamoto – "Sukiyaki"
Napoleon XIV – "They're Coming to Take Me Away, Ha-Haaa!"
Caramba - "Hubba Hubba Zoot Zoot"
Hot Butter – "Popcorn"
Carl Douglas – "Kung Fu Fighting"
The Boomtown Rats – "I Don't Like Mondays"
The Weather Girls – "It's Raining Men"
Frankie Goes to Hollywood – "Relax"
Harold Faltermeyer – "Axel F"
Baltimora – "Tarzan Boy"
Falco – "Rock Me Amadeus"
T'Pau – "Heart and Soul
Sabrina - "Boys, Boys, Boys"
Technotronic – "Pump Up the Jam"
Alannah Myles – "Black Velvet"
Shakespears Sister – "Stay"
Haddaway – "What Is Love"
Beck – "Loser"
Aqua – "Barbie Girl"
Eiffel 65 – "Blue (Da Ba Dee)"
Kaoma – "Lambada"
Right Said Fred – "I'm Too Sexy"
Now, taking a look at stuff I listed... I'm not even gonna tell how many I had on cassettes...