I’m unclear if the OP means highly regarded bands with many hits where you only like one song, or any band where you only like one song.
Grauzone - Eisbaer
With one album to their name and nothing on it compares to this song, which is on endless compilations.
Can I offer a megahit dude with, IMHO, only two songs I can stomach (indeed, I actual like them)?
Elton John, “Rocket Man” And “Goodbye Yellow Brick Road”.
My awareness of Jane’s Addiction is only vague. I may or may not have heard the song in question, but I want you to know that I really and truly like what you’ve written here.
Regarding the thread:
Jackson Browne - Lawyers in Love
You don’t like any Pointer Sisters songs then. That one was by Sister Sledge.
Collective Soul - Shine.
Butterfly Bleu was amazing but nothing else Iron Butterfly did was noteworthy.
Well, I would think Golden Earring rules this thread with “Radar Love” and “Twilight Zone”. . . but that’s two. . . but, two songs I consider true greats and I’ve never heard another song by them or listened to any of their records. But, that may be the problem.
Heresy ! What about “Pinball Wizard”, “Behind Blue Eyes”, “Won’t Get Fooled Again”, “Who Are You”, etc., etc. !
I would say “Eagles”, but “Life in the Fastlane” (I think because there are multiple Eagles replies, each with different songs, it excludes them from this OP)
Also “ELO” “Fire on High” (I don’t like any of their vocals !)
I’ll vote for “Werewolves of London” by Warren Zevon, although I have to admit that I haven’t listened to dozens of Warren Zevon songs.
Pink Floyd - Another Brick in the Wall
Nope,* Lawyers Guns and Money* is the only good Warren Zevon song.
Falco - “Rock Me Amadeus”
I disagree with almost every post here.
Aerosmith? How about “Draw the Line”, “Sweet Emotion”, or “Walk This Way”?
Nirvana? How about “Breed”, “Territorial Pissings”, “About a Girl”, or “All Apologies”?
Pink Floyd? What about the entire Dark Side of the Moon, The Wall, and Wish You Were Here albums?
To me The Eagles are the Alan Jackson of country rock. I like just about every one of their songs, they’re pretty non-objectionable. I especially like “Peaceful Easy Feeling”, “Desperado”, and “Take it Easy.”
AC/DC, what about “Dirty Deeds Done Dirt Cheap”, “Shoot to Thrill”, and “Highway to Hell”?
Take a listen to Der Kommissar and Jeanny.
I like Falco but I think you are missing the point of this thread. Falco is a one-hit wonder outside of Europe.
Yer both wrong. “My Shit’s Fucked Up” is the only Zevon song worth listening to
besides all of 'em.
I have listened to Der Kommisar and Jeanny. I thought Der Kommisar was a hit in the US, and Vienna Calling. Perhaps my being in college radio in the mid-80’s has colored my perceptions.
Every time the guys on the radio talk about “all the albums” made by Led Zepplin, I get really disoriented and say to myself, “Oh. Did Led Zepplin do another song besides Stairway to Heaven?”
“Rock Me Amadeus” hit #1. Vienna Calling got as high as #18 on the Billboard Hot 100. “Der Kommisar” only made it to #72 on the Hot 100. The cover by After the Fire is the one that was a hit in the US (peaking at #5.)
No, no, no, no, etc., etc.! Do not like. Also note that I didn’t put a Rush song on here because there isn’t a single song of theirs I like at all. Bring it! 
Thought of another one:
Elvis Costello - Alison
**Taylor Swift **- Whatever that song from Hunger Games she did w/ the Civil Wars is pretty great.