Norman Greenbaum and Katrina and the Waves come to mind. Is there anyone who actually hit no. 1 and never had another significant hit?
Bonus points for having a hit that is still played today.
Minus points for avoiding other hits by dying.
“Video Killed the Radio Star” by the Buggles comes to mind.
Steam’s “Na Na Hey Hey Kiss Him Goodbye” was #1 for two weeks and is still popular today.
Doctor and the Medics, Spirit in the Sky. They’re still performing it today - right here in my town next week - and they do it at the end of the set because it often lasts for an hour.
Zager and Evans “In the year 2525” comes to mind also.
Geeze, they sucked!
According to this site, http://www.aventis.com/future/fut0202/in_the_year_2525/in_the_year_2525_1.htm
Green Eyed Lady - Sugarloaf
Everybody’s Talking At Me - Harry Nilsson
Keep Your Hands to Yourself - Georgia Satellites
When VH1 did their obligatory countdown, “Macarena” topped the list.
Unless you count Jimi Hendrix, who for all his success only had ONE single reach the top 20 (I forget which one.)
“All Along the Watchtower”
I have an MPG of that vid. It makes me laugh everytime I watch it!
IIRC Norman Greenbaum wrote a bunch of hits for 38 Special among others.
Here’s some other good ones:
Plimsouls-“Zero Hour”. I still hear it on the local “Modern Rock” (Lets not get into THAT) station every once in awhile.
Belfegore-“All That I Wanted”- A German-American-Canadian trio who missed the nu-metal-pop-disco bandwagon by about 15 years. I keep hoping VH1 Classic will play the video while I’m watching.
The mother of ALL one hit wonders: Wall Of Voodoo-“Mexican Radio” EVERYBODY knows this song, but nobody knows who WoV are. Thats sad. Everyone should own at least one Wall Of Voodoo album.
Jon
That’s the answer. They did have a follow-up single, “Mr. Turnkey,” but it failed to make Billboard’s Hot 100. This song was about a chap in jail in Wichita Falls for having committed a rape.
BTW, I always thought it was kinda interesting to hear Norman Greenbaum singing “Gotta have a friend in Jesus.” But then again, the best-selling Christmas song of all time was written by Irving Berlin.
Nilsson had several other hits, most notably Without You.
Haj
The Plimsouls also had “Million Miles Away” from that Valley Girl movie.
In the same vein, Modern English with “I Melt With You”.
Dexy’s Midnight Runners - “Come On Eileen”
Animotion - “Obssession”
Icicle Works - “Whisper To A Scream”
The Honeydrippers - “Sea of Love”
Flock of Seagulls - “I Ran (So Far Away)”
The 50s also had their share of flash-in-the-pan groups. The girl that sang “It’s My Party” comes to mind.
“Biggest” is certainly a all-encompassing term. Zager and Evans may have sold more overall(although I don’t see how;it’s a depressing song, and,thankfully you never hear it anymore), but Debbie Boone’s You Light Up My Life sat at the number one spot for 10 weeks. If she had anything resembling a hit after that, I’ve never heard of it.
Chris W
i like the Z&E tune in the year 2525
Wasn’t that Lesley Gore? I can easily think of two of her other songs - Judy’s Turn to Cry (may not be the real name) and You Don’t Own Me.
THANK YOU. I was telling someone recently that only one group had ever had a number one single without ever hitting the top 100 again. I could remember nothing except their follow up single was an ode to, I believe, a guilty rapist. Now I know which greats achieved this feat.
Strawberry Alarm Clock - “Incense and Peppermints”
“Macarena”, followed by Bizet’s Carmen. If you want a one-hit wonder, you can’t go wrong with either of these two.
There are plenty of one-hit wonders from which to choose.
Rick Dees and “Disco Duck” come to mind…
I went to a party the other night
All the ladies were treatin’ me right
Movin’ my feet to the disco beat
how in the world could I keep my feet?
All of a sudden I began to change
I was on the dance floor actin’ strange.
Quack
quack! Flappin’ my arms
I began to cluck
Quack!
Look at me
I’m the Disco Duck!
Sing along all…Disco…disco duck 
NOW for the all time one hit wonder. How about The Owen Bradley Quintet
They had one hit, that’s all. And Owen Bradley still made it the Country Music Hall of fame. (but as a producer)
I don’t know if they’d be considered a 1hw but WAR has been riding that low rider for a long time now.
quack-quack
Maybe just choose any group from the 80’s and throw a dart? 
('67 - '70)
The Unicorn - Irish Rovers
Spooky - Classics IV
In-A-Godda-Da-Vida - Iron Butterfly
Gimme Some Lovin’ - Spencer Davis Group
To Sir With Love - Lulu
A Whiter Shade Of Pale - Procul Harum
War - Edwin Starr
In The Summertime - Mungo Jerry
Rubber Ducky - Ernie (Sesame Street) - (laughing my ass off here right now)
Build Me Up Buttercup - Foundations
Venus - Shocking Blue
I Got A Line On You - Spirit
Tighten Up - Archie Bell and the Drells
(Hendrix - Purple Haze never made the top 10?)