Adam Ant. Probably really only known in the US for Goody Two Shoes. Adam Ant - Goody Two Shoes - YouTube
He’s done a lot more -and of course he used to be in Adam and the Ants, and I like his Manners & Physique album. Here’s Room at the Top:
Yep, after listening to the album, that was the one I predicted would be the huge follow-up hit. It peaked at #86. “Red Light” was great as well - never heard that one even on the rock stations, except on the weekday noon show where they would play an entire album side (“Side Orders For Lunch” was the show’s name).
The US punk/new-wave stations played One Step Beyond quite a bit, but still, I think that and Our House was the only Madness I ever heard on commercial radio. The college stations, on the other hand…
Like a lot of other posters, I’m not sure these would be ‘one hit wonders’, but definitely get less airplay than they deserve on various rock/classic rock/alternative rock stations.
For XTC, I love Skylarking (yes, it’s the most pop/commercial of their work) but more people that I’ve spoken too remember ‘The Ballad of Peter Pumpkinhead’ more than ‘Dear God’ or ‘Mayor of Simpleton’ - so popular songs over at least 3 albums. Yeah, their albums didn’t normally crack the top 40 in the us, but they have 3 that hit the top 50. And of course, much more recognition in the UK.
For Midnight Oil, I think ‘Beds are Burning’ is considered their one hit from Diesel and Dust, I preferred Blue Sky Mining and Earth Sun and Moon more. Diesel and Dust as well as Blue Sky Mining were both top 40 in US, and Earth Sun and Moon was 49.
Oingo Boingo is probably the best fit of the three for one hit wonder, but when I think of them it’s “Dead Man’s Party” that comes to mind before “Weird Science.” Then again, it was really popular with my late 80s/early 90s group of friends who were into ‘darker’ music. If I recall, it was even quoted in my First Edition Vampire the Masquerade game.
A fanatstic band, they had moderate early UK success with “We’re Only Makng Plans For Nigel” going to no.17. Too bad “Life Begins at the Hop” came in at only 54, and with neither, yeah, registering across the pond, hence the bolding.
Came to mention Dave Edmunds but four or five posters have beaten me to it and hopefuly so by this point in the thread.
Repeat When Necesary is quite a loaded album.
heh…and speaking of loaded…for a somewhat ironic, or inverted, take on the OP…
The Velvet Underground’s Loaded album was called that with the intention of making it an album “loaded” with potentioal radio hits that roughly clock in in three minutes or less - a major departure from their extendo song structure. (Well, they also tied in the other “loaded” definition too, of course)
If “Head Held High” isn’t the most toe-tappingest kick-bum number ever, my name’s Margaret Meehan (Parkdale).
Nothing registered in the charts.
Their later albums were more accessible. Their album “10, 9, 8 [etc] 1” would be considered their best by many Midnight Oil aficionados (known as “Oilers” here).
Yet another example of an artist who had a more successful career outside the United States. I like his song “Hyperactive” better and it managed to break the top 20 in the UK.
“Run Runaway” is what I remember them for and according to Wikipedia is peaked at #20 in the US in 1984. It wasn’t until the last 10-15 years that I learned they originally sang “Cum on Feel the Noize” but since it was originally released a few years before I was born I hope I can be forgiven for that. I just remember the song because it’s one of those oddities from the 80s that occasionally gets stuck in my head. (And I see someone else already mentioned “Run Runaway.”)
I didn’t know any of their other songs until Youtube became a thing and I quite like them.
Just to confuse the issue, Dave Edmunds released an album titled Rockpile before teaming up with Lowe and forming a band named Rockpile.
Iirc, the Zombies had a big hit with “She’s Not There”, and then a smaller hit with “Tell Her No”, then a few years later had “Time of the Season”. They were always good, just not chart toppers.
Oh My God! Why this band wasn’t ‘The Second Beatles’ …
Great music. So much more than Time of the Season and so forth.
Epic case of under-promotion.
Didn’t break the top 20, but I love Europa and the Pirate Twins:
I’d replace with “other decent” with “much better” as a question, and provide
Chumbawamba.
Famous for THAT song, it’s the worst song on their worst album. At a low in their careers, they were kicked off their label with 50K of debt from recording their new album, and signed to EMI (Germany), who they hated, but were desperate. EMI, did their stuff and it’s one of the most played songs in the world.
They’ve released 16 studio albums, and the ones which quietly unsold after Tubthumper were wonderful and so much better. Most of the ones before were great too (though not so fond of Anarchy).
They’ve not played the game, at least two of the main songs from their later albums got offers to be used in adverts for cars and other things, and they always refused, so they could have been more famous than they were.
Half the band left around 2005, and they continued acoustically in small venues around the UK. We saw them in a tiny place in Stourbridge around 2010. I can’t recall if they even played Tubthumper.
They finished off in 2012. I believe the royalties from that single alone keeps the ten odd members very well off and feel no need to make more music.
My son played “Gold” by Spandau Ballet for me. It’s better than “True”, their one big hit that has been on every 80’s New Wave compilation since 1992.
Here’s a good one:
Trivia fun fact: People were a one-hit wonder for “I Love You,” a Zombie’s b-side written by bassist Chris White. An oddity, but a terrific one.
I’m glad this thread is here, I was thinking about starting one but couldn’t figure out the right premise.
At any rate, I can think of a couple of bands, oddly from the late 90s because my memory was jogged by another one-hit-wonder thread, for whom I preferred their follow-up single.
Fastball: you couldn’t escape “The Way” in 1998 but “Fire Escape” was just as great.
Semisonic: “Closing Time” was huuuuuuge but “Singing in my Sleep” is a much more solid track, IMHO.
I’m at work so I’m only doing this with half a brain…I’ll chime in again later if I can think of other big examples.
Faith No More does not qualify for this thread. They had 2 songs that made the top 100, Epic reached #21 and was a much bigger hit than the song Easy that only made it to #58. Epic still get plenty of plays on classic radio stations, I haven’t heard Easy in years.
I feel chastened 
I knew of both “Epic” and “Easy” for a long time before I realized that they were both by the same group. The vibe of the two songs are so different that I just figured “Epic” was by more of a hard-rocking group and “Easy” was recorded by an easy-listening artist.
The OP specifies a “group” – does a singer count? Many years ago, there was a similar thread on the Straight Dope, and that thread introduced me to Joan Osborne. One-hit wonder with “What If God Was One Of Us?”, but lots of other catchy songs that really show off her vocal talent.