Harvey Danger - Flagpole Sitta. The album, Where Have All the Merrymakers Gone, is fantastic. And the song has some of the most poetic lyrics about masturbation:
Fingertips have memories
Mine can't forget the curves of your body
And when I feel a bit naughty
I run it up the flagpole and see who salutes
(But no one ever does)
Thomas Dolby - She Blinded Me with Science; IMO, an okay song. However, the album The Golden Age of WIreless is very good. Technically, I believe he had at least one other hit but people remember that first song. Also had a career producing (notably for Prefab Sprout!) and founded a tech company.
Gary Numan - Cars; again, not his only hit but what is remembered. The Pleasure Principle is awesome. Songs like Complex and Films are stellar. His work with his first band, Tubeway Army, is also worth a listen.
@Melt Face Molly Drop i grabbed New Radicals on vinyl when there was some Sound of Vinyl sale or something and I forgot how good that album is. I had the CD growing up and I remembered every word
Better Than Ezra is know for the song “good” but they actually have a pretty extensive discography of which the first 3 albums are pretty great.
Cowboy Mouth known for “Jenny says” was a pretty good band and super fun live.
KMFDM - best known for "Juke Joint Jezebel" off of Nihil. The song was furthered by its use in the movies Bad Boys & Mortal Kombat. The song reached 27 on Billboard's Dance Club Songs. I stopped listening after the departure of En Esch & Gunter Schulz but they were a huge band for me from about the ages 12-15. I'll argue that they should be included on the "Mt Rushmore of industrial groups". Rip the System!!!