I hardly think foreign bands who happened to get credit once in the States should count (e.g. Falco, A-ha, Midnight Oil, Los Del Rio). In fact, the ones who produced lots of great music but fell to the whims of a fickle public are highly questionable. And don’t get me started on non-pop bands who have only one “mainstream” hit (hello, Everything But the Girl!) IMHO, a real] one hit wonder is a complete flash in the pan, someone who was never known for anything else.
Anyhoo…some of the more memorable ones.
Johnny Hates Jazz, Shattered Dreams. Standard bitter breakup song. Even more standard complete fade into oblivion afterward.
Sheriff, When I’m With You. Somewhat sappy love song a la REO Speedwagon or Chicago. Dunno why some hit it big and some don’t.
Take That, Back For Good. A pretty good pop single from a “boy band” that never caught on. And this was well before the enormous backlash began.
After the Fire, Der Komissar. Somewhat confusing Americanized version of Falco’s hit. Never heard from again afterward. (Note: A “kommissar”, in the early 20th century, was a Soviet official assigned to enforce Communism amongst the masses. From what I’ve heard, they weren’t too popular.)
Chumbawamba, Tubthumping. The funny thing is, they never even wanted to have a hit 'cause they’re anarchists. Fight the power, don’t accept anything from The Man, etc. The Man deigned to give them their big break regardless.
Boy Meets Girl, Waiting For a Star to Fall. Beautiful song. Moving but not sappy and great to listen to.
Soul Sister, The Way to Your Heart. Would have never even heard of this song if a couple of radio hosts didn’t have a real fondness for it. I never found any of their albums in any store, and this was the only song of theirs I could ever find anywhere.
And before anyone even mentions M.C. Hammer, remember, 2 Legit 2 Quit was a pretty big follow-up to U Can’t Touch This. (I kinda miss him…he was the first rapper I actually liked.)
As long as we are pointing out all the two-hit wonders (and there are a lot of them), here are a couple:
General Public, Tenderness and I’ll Take You There. Britpop band. Saw about half of the music video for the former once in my life. Never heard once on the radio. Heard the latter from a commercial which I don’t even remember. Both songs now on my computer. I love this modern age. 
Tracy Chapman, Fast Car and Give Me One Reason. Remarkable mainly because so much time passed between them (same for Never Surrender and Sunglasses at Night).
It’s bizarre the kind of songs that become hit… I have eight Aqua songs on my computer right now, and as far as I’m concerned they all absolutely blow Barbie Girl out of the water. I also liked Cross My Heart a lot better than the too-freaking-confusing-to-be-depressing Toy Soldiers. (And HOW the hell is it supposed to be about drug addiction??)
Just a footnote: I watched a few one hit wonder specials on VH1. If you have the time to watch one, do; they’re real eye-openers. It’s amazing how many bands had a great thing going and then just broke up for some stupid reason.