I saw Toad on their reunion tour about two or three years ago. They were awesome. I’d been catching Glen Phillips’ shows for a while, and they got back together out of the blue. for a tour or two.
I often hear “Good Intentions” on the adult easy listening station here in Austin…
T’Pau had a bigger hit on this side of the world with “China In Your Hand”.
Sigue Sigue Sputnik had a hit Love Missile F1-11. They released an album in 2003 to no acclaim whatsoever.
“This Town Ain’t Big Enough for Both of Us” by Sparks
(The Brothers Mael are still kickin’, and they’ve got a heck of a concert series planned in London this year.)
Sparks had a hit in the early 1990s with “When Do I Get To Sing My Way?”
Seven Mary Three was a one-hit wonder in the 90s, as was Primitive Radio Gods. Neither were altogether bad bands. Also, Saigon Kick was pretty decent.
From the 80s, I give you When In Rome. You do remember The Promise, don’t you?
I have a distinct memory of an early-90s MTV commercial that touted three new bands and their songs. They were:
Rage Against the Machine: went on to be one of the world’s biggest and most controversial bands for years, and - unfortunately - helped usher in the whole nu-metal thing. The song was Freedom.
Us3: a one-hit wonder, but still, their one hit - the jazz-rap hybrid Cantaloop (Flip Fantasia) was an enormous hit in 1993 and a pretty cool song.
Deep Forest: Nope! I’m guessing the song was Sweet Lullaby, but even while the commercial was playing I couldn’t have told you anything about the song.
Anyone else remember The Spys? I have the LP “Behind Enemy Lines” downstairs in the basement. They might have even had a second one. The other video I remember from MTV (back when the played videos - yes, I’m a crotchedy old bastard and get off my lawn) was for “She Can’t Wait”. It sounds a bit dated to my ears these days. But I’m into a bit more pared down sound. And, believe it or not, these guys are not to be found on YouTube.
I remember buying the album, the guy at the record store was like “The Spys?” And he walks over to the import section, like it was some freaky European band, like The Clash or Duran Duran.
Of course, it was used in the end credits of “Napolean Dynamite” 
The makers of that film were also kind enough to slide Alphaville’s “Forever Young” into the school dance scene.
GTR also had a song called “The Hunter”. Is it possible the OP has somehow mangled that into a band name?
Back in the day, National Lampoon magazine would print humerous reader-submitted photos. One classic was a marquee from some outdoor venue that showed a double billing. It read like this:
JULY 22
SQUEEZE
THE HOOTERSI was going to say The Squeeze.
Also, Big Star and The Jesus and Mary Chain.
What about Gin Blossoms?
“Why Me” by Planet P.
BTW, a few years ago I bought a used copy of Planet P’s concept double-LP Pink World. Obvious attempt to sound like Pink Floyd, both in their trippy, heavily-produced sound, and their Roger Waters-esqe guitar ballads. When I played if for my friend, who is heavily into Floyd/Roger Waters, halfway through she was saying, “Boy, Roger Waters is a genius”. I had to remind her, “No, this is not Roger Waters. Like I said, it’s Planet P”.
Ugly Kid Joe
Nitzer Ebb
The Wonder Stuff
Veruca Salt
The Stone Roses
Faith No More
Ministry
The early nineties were ripe with these bands.
Do you mean Difford/Tilbrook Squeeze? If so I’ll have to disagree. Everybody knows “Tempted,” though if you ask them who sang the song, you’ll probably get blank stares.
Hip-hop fans: I thought Awesome Dre and the Hardcore Committee were great back in the late 80s, and when Detroit blew up I thought they’d get some love. No chance!
How about Animotion? UK 80s bootwearers King? 90s embarrassments Londonbeat? Art of Noise? JoBoxers?
Here’s a band that was immensely popular, but they are hardly ever mentioned anymore: Fine Young Cannibals. I think most people remember them, but you’d think you’d hear their songs on the radio, or in commercials more.
This is a valid point.
I remember them – they had two bass players, right? That reminds me of another awesome band no one seems to remember: Cop Shoot Cop. For years, they had no guitars – just drums, two basses, and a sampler.
King Crimson.
No way. Very fervent, active fan base; a steady stream of archival releases and downloads, and the band itself is just coming out of a period of inactivity to try out its new lineup on the road.
I just did a search on my local classic rock station (KFOG), and found that they played it less than two weeks ago.