I think I can name a few....
"10-9-8" by Face To Face (who had a big dance hit with "Under the Gun")
"19" by Paul Hardcastle (who had several hits in the U.K.)
"99 Luftballons" by Nena (who was very successful in her native Germany)
"All I Need" by Jack Wagner
"All Our Tomorrows" by Eddie Schwartz (who had other hits in Canada)
"And I'm Telling You (I'm Not Going)" by Jennifer Holliday
"Angel Eyes" by Jeff Healey Band (who had several hits in Canada)
"Another Lover" by Giant Steps (who had several dance hits as The Quick)
"As We Lay" by Shirley Murdock
"Axel F" by Harold Faltermeyer
"Baby Come to Me" by Patti Austin (with James Ingram, who is not a one-hit wonder)
"Baby, I Lied" by Deborah Allen (who had several country hits)
"Baby Love" by Regina (who had another dance hit)
"The Ballad of Jayne" by L.A. Guns
"Beat's So Lonely" by Charlie Sexton (who worked with the likes of Bob Dylan, and Keith Richards as a session musician)
"Beds Are Burning" by Midnight Oil (who is an Australian band that had another hit in the U.K., and major success in Australia)
"Boys Night Out" by Timothy B. Schmit (who was a member of The Eagles and Poco)
"Burning Heart" by Vandenberg
"Call Me" by Skyy (who had several R&B hits)
"Call to the Heart" by Giuffria
"Can't Shake Loose" by Agnetha Faltskog (who was a member of ABBA)
"The Captain of Her Heart" by Double
"Chariots of Fire — Titles" by Vangelis (who also had a few hits in Europe)
"The Clapping Song" by Pia Zadora
"Come on Eileen" by Dexys Midnight Runners (who had several hits in the U.K.)
"Cry" by Godley & Creme (who were former members of the band 10cc, who had several hits of their own in the U.K.)
"Cry" by Waterfront
"Cuddly Toy (Feel for Me)" by Roachford (who had several hits in the U.K.)
"Curly Shuffle" by Jump 'n' the Saddle Band
"Da'Butt" by E.U. ("E.U." is short for Experience Unlimited, who had a few other R&B hits)
"Der Kommissar" by After the Fire (English cover version of a German hit by Falco)
"Desert Moon" by Dennis DeYoung (who was Styx's lead singer and keyboardist)
"Digging Your Scene" by The Blow Monkeys (who had several hits in the U.K.)
"Don't Close Your Eyes" by Kix
"Don't Disturb This Groove" by The System (who had several dance hits)
"Don't Give It Up" by Robbie Patton (who worked with Fleetwood Mac in the late 1970s. He was produced by Mac keyboardist Christine McVie, and Mac guitarist Lindsey Buckingham played on this track)
"Don't Leave Me This Way" by The Communards (whose lead singer Jimmy Somerville previously fronted Bronski Beat; they had more hits in Europe)
"Don't Let Him Know" by Prism (who had several hits in Canada)
"Don't Make Me Over" by Sybil (who had several dance hits)
"Don't Stop the Music" by Yarbrough and Peoples (who had several dance hits)
"Don't Worry Be Happy" by Bobby McFerrin
"Double Dutch Bus" by Frankie Smith
"Downtown" by One 2 Many
"Easy Lover" by Philip Bailey (with Phil Collins, who is not a one-hit wonder. Bailey was a member of Earth, Wind & Fire)
"Edge of a Broken Heart" by Vixen
"Everlasting Love" by (Rex Smith/)Rachel Sweet (Smith is not a one-hit wonder)
"Everybody Dance" by Ta Mara and The Seen
"Everybody's Got to Learn Sometime" by The Korgis
"Facts of Love" by Jeff Lorber (featuring Karyn White, who is not a one-hit wonder)
"Fantasy" by Aldo Nova
"Far From Over" by Frank Stallone
"Fascinated" by Company B
"Feel It Again" by Honeymoon Suite (who had several hits in their native Canada)
"Fishnet" by Morris Day
"Flames of Paradise" by Jennifer Rush (with Elton John, who is not a one-hit wonder. Rush had several other hits in Europe)
"For Tonight" by Nancy Martinez (who had had other hits in Canada)
"Friends" by Eric B. and Rakim (with Jody Watley, who is not a one-hit wonder. The duo had more success on the hip-hop charts)
"Friends and Lovers" by Gloria Loring and Carl Anderson
"The Future's So Bright, I Gotta Wear Shades" by Timbuk 3
"Funkytown" by Pseudo Echo
"Funkytown" by Lipps Inc.
"Gee Whiz" by Bernadette Peters
"General Hospi-Tale" by The Afternoon Delights (this song was recorded by session musicians, and was never intended to be followed up)
"Genius of Love" by Tom Tom Club (which was a side project of Talking Heads members Chris Frantz and Tina Weymouth)
"A Girl in Trouble (Is a Temporary Thing)" by Romeo Void
"Girls with Guns" by Tommy Shaw (who is better known as a member of Styx, and Damn Yankees)
"Giving It up for Your Love" by Delbert McClinton
"Goin' Down" by Greg Guidry
"Grandma Got Run over By a Reindeer" by Elmo and Patsy
"Hanging on a Heart Attack" by Device
"Heart and Soul" by T'Pau (who had several hits in the U.K. and Europe)
"Heaven Help Me" by Deon Estus (with George Michael, who is not a one-hit wonder; Estus was a member of Michael's supporting band)
"Holiday" by The Other Ones
"Holdin' On" by Tané Cain
"Honestly" by Stryper
"The Honeythief" by Hipsway
"Hooked on Classics" by Louis Clark conducting the Royal Philharmonic Orchestra
"Hooked on Swing" by Larry Elgart and His Manhattan Swing Orchestra
"How Do I Survive" by Amy Holland
"I.G.Y. (International Geophysical Year)" by Donald Fagen (who is a member of Steely Dan)
"I've Never Been to Me" by Charlene
"I Beg Your Pardon" by Kon Kan
"I Believe in You" by Don Williams (who had many hits on country charts)
"I Couldn't Say No" by Robert Ellis Orrall with Carlene Carter
"I Do What I Do" by John Taylor (who was Duran Duran's bassist)
"I Don't Mind At All" by Bourgeois Tagg
"I Know There's Something Going On" by Frida (who was a member of ABBA)
"I Loved 'Em Every One" by T.G. Sheppard
"I Remember Holding You" by Boys Club
"I Wanna Be a Cowboy" by Boys Don't Cry
"I Want You, I Need You" by Chris Christian
"I'm Happy That Love Has Found You" by Jimmy Hall
"I'm Losing You" by Uptown
"If I Had My Wish Tonight" by David Lasley
"If The Love Fits Wear It" by Leslie Pearl
"Iko Iko" by Belle Stars
"In a Big Country" by Big Country (who had other hits in the U.K.)
"In My House" by Mary Jane Girls (who had a hit on the R&B charts with "All Night Long" in 1983)
"Into the Night" by Benny Mardones (this song was a one-hit wonder twice: in [980 and 1989)
"Invisible" by Alison Moyet (who was the lead singer of Yazoo, and had many solo hits in the U.K. This was one of her lesser U.K. hits.)
"Is It You" by Lee Ritenour (who has had many hits on jazz charts)
"It Takes Two" by Rob Base and DJ E-Z Rock
"It's Now or Never" by John Schneider
"Just Got Lucky" by JoBoxers
"Just So Lonely" by Get Wet
"Just the Two of Us" by Grover Washington, Jr. (with Bill Withers, who is not a one-hit wonder)
"Keep Your Hands to Yourself" by The Georgia Satellites
"Key Largo" by Bertie Higgins
"King of the Hill" by Rick Pinette And Oak
"Kiss and Tell" by Bryan Ferry (who is the lead singer of Roxy Music and had many solo hits in the U.K.))
"Kiss Him Goodbye" by The Nylons (who had other hits in Canada)
"Let Go" by Sharon Bryant
"Let's Go All the Way" by Sly Fox
"Let It Whip" by The Dazz Band
"Let the Music Play" by Shannon
"Lies" by Jonathan Butler
"Live is Life" by Opus
"Living in a Box" by Living in a Box (who had other hits in the U.K.)
"Lookin' for Love" by Johnny Lee
"Love Changes (Everything)" by Climie Fisher (who had other hits in the U.K.)
"Love Plus One" by Haircut 100 (who had other hits in the U.K.)
"Love Theme from St. Elmo's Fire" by David Foster
"Love You Like I Never Loved Before" by John O'Banion
"A Lover's Holiday" by Change
"Major Tom (Coming Home)" by Peter Schilling (who had other hits in his native Germany)
"Mama Used to Say" by Junior
"Mary's Prayer" by Danny Wilson
"Miami Vice Theme" by Jan Hammer (who is best known for his work on Miami Vice; another Hammer track from the series, Crockett's Theme, was also a hit in the U.K. and Europe)
"Mickey" by Toni Basil
"Mister Sandman" by Emmylou Harris (who has had many hits on the country charts)
"Modern Day Delilah" by Van Stevenson
"More Than Just the Two of Us" by Sneaker
"Motortown" by Kane Gang (who had several hits in the U.K.)
"Murphy's Law" by Chéri
"My Ever Changing Moods" by The Style Council (who had other hits in the U.K.)
"My Girl" by Suave'
"Need You" by Donnie Owens
"The Never Ending Story" by Limahl (who was the lead singer of Kajagoogoo)
"New Romance (It's a Mystery)" by Spider
"Nice Girls" by Eye To Eye
"Nicole" by Point Blank
"Nightbird" by (Stevie Nicks with) Sandy Stewart (Nicks is not a one-hit wonder)
"Nobody" by Sylvia (who had other hits on the country charts)
"Nobody Said It Was Easy (Lookin' for the Lights)" by LeRoux (who also had a huge regional hit with "New Orleans Ladies" in 1978 which peaked at fifty-nine)
"Not Just Another Girl" by Ivan Neville
"Object of My Desire" by Starpoint
"On the Loose" by Saga (who had many hits in Canada)
"One Step Closer to You" by Gavin Christopher
"Operator" by Midnight Star (who had bigger success on the R&B charts)
"Out of Mind, Out of Sight" by Models
"Pac Man Fever" by Buckner and Garcia
"Pass the Dutchie" by Musical Youth (who had other – though less well-remembered – hits in the U.K.)
"Perfect Way" by Scritti Politti (who had other hits in the U.K.)
"Personally" by Karla Bonoff
"Pilot of the Airwaves" by Charlie Dore
"The Politics of Dancing" by Re-Flex
"Precious to Me" by Phil Seymour
"The Promise" by When in Rome
"Pump up the Volume" by M/A/R/R/S
"Puttin' on the Ritz" by Taco Ockerse
"Radioactive" by The Firm (The Firm featured Jimmy Page (Led Zeppelin), and Paul Rodgers (Bad Company) in its lineup)
"The Rain" by Oran "Juice" Jones
"Rapper's Delight" by Sugarhill Gang
"Relax" by Frankie Goes to Hollywood (who were a far more successful act in the U.K.)
"Respect Yourself" by Bruce Willis
"Right on Track" by Breakfast Club
"Ritual" by Dan Reed Network
"Rock and Roll Dreams Come Through" by Jim Steinman
"Rock On" by Michael Damian
"Romeo's Tune" by Steve Forbert
"Round and Round" by Ratt
"Rumors" by Timex Social Club
"Rush Hour" by Jane Wiedlin (who had many hits as a member of The Go-Go's)
"Sausalito Summernights" by Diesel
"Savannah Nights" by Tom Johnston (Johnston was a founding member of The Doobie Brothers; he left the band in 1977, but rejoined it when it reformed in 1988)
"Sayin' Sorry (Don't Make It Right)" by Denise Lopez
"The Seduction (Love Theme from American Gigolo)" by the James Last Band (Last had many hits in Europe, especially in his native Germany)
"Serious" by Donna Allen
"Set Me Free" by Utopia (Utopia was formed by Todd Rundgren)
"Seven Year Ache" by Rosanne Cash
"Shake You Down" by Gregory Abbott
"She's Like the Wind" by Patrick Swayze featuring Wendy Fraser
"She Blinded Me with Science" by Thomas Dolby
"Ship of Fools (Save Me from Tomorrow)" by World Party
"So Alive" by Love and Rockets (who had several U.K. hits)
"Somebody's Knockin'" by Terri Gibbs
"Soul City" by Partland Brothers
"Stand by Me" by Mickey Gilley (who had numerous hits on the country charts.)
"Strange but True" by Times Two
"Stronger Than Before" by Carole Bayer Sager (who is a one hit wonder in the U.K., but with a different song.)
"Sugar Don't Bite" by Sam Harris
"Sugar Free" by Wa Wa Nee
"Supersonic" by J. J. Fad
"Surrender to Me" by Robin Zander (Sung with Ann Wilson, one of the two sisters who formed Heart. Zander was the lead singer of the popular band Cheap Trick.)
"Sweet Baby" by Stanley Clarke and George Duke (Clarke is a well-known jazz musician, while Duke is a well-known funk musician who had other hits on the soul charts)
"Swing the Mood" by Jive Bunny and the Mastermixers
"Tainted Love" by Soft Cell (who had other hits in the U.K.)
"Take a Little Rhythm" by Ali Thomson
"Take Off" by Bob and Doug McKenzie, featuring Geddy Lee of Rush
"Take Your Time (Do It Right), Part 1" by The S.O.S. Band (who had several other hits on the R&B and dance charts)
"Talk It Over" by Grayson Hugh
"Talk to Me" by Chico DeBarge (DeBarge was a member of his family's hit-making band, DeBarge)
"Tarzan Boy" by Baltimora
"Tender Love" by Force M.D.'s
"Thanks for My Child" by Cheryl Pepsii Riley
"That's Love" by Jim Capaldi (who had many hits as a member of Traffic)
"Theme From Greatest American Hero (Believe It or Not)" by Joey Scarbury
"There's No Stoppin' Us" by Ollie and Jerry (who were also members of hit act Raydio)
"They Don't Know" by Tracey Ullman (who had several hits in the U.K.)
"Thinking of You" by Safire
"Tired of Toein' the Line" by Rocky Burnette
"Together" by Tierra
"Tomorrow People" by Ziggy Marley and the Melody Makers
"Too Shy" by Kajagoogoo (who had several other hits in the U.K. Their original frontman, Limahl, was also a U.S. one-hit wonder in his own right.)
"Tragedy" by John Hunter
"Tuff Enuff" by The Fabulous Thunderbirds
"Turning Japanese" by The Vapors
"Turn up the Radio" by Autograph
"Two Occasions" by The Deele
"Under the Milky Way" by The Church (who had other hits in their native Australia and the U.K.)
"Video Killed the Radio Star" by The Buggles
"Wait For You" by Bonham
"Wake Up (Next to You)" by Graham Parker and The Shot (who had other hits in the U.K.)
"We Are The World" by USA For Africa
"We're Not Gonna Take It" by Twisted Sister
"What About Me" by Moving Pictures
"What Are We Doin' In Love" by Dottie West (with Kenny Rogers, who is not a one-hit wonder; West had many hits on the country charts)
"What I Am" by Edie Brickell and New Bohemians
"Wild Wild West" by The Escape Club
"Welcome to the Boomtown" by David and David
"When I'm with You" by Sheriff (This became a U.S. hit when re-released in 1989; it had been a hit in their native Canada six years earlier, "More Than Words Can Say" became a hit in 1990 under the band name Alias.)
"When the Heart Rules the Mind" by GTR + *"When the Heart Rules the Mind" by GTR (band led by former Genesis guitarist Steve Hackett and former Yes and Asia guitarist Steve Howe)
"When We Kiss" by Bardeux
"When Your Heart Is Weak" by **** Robin (who had other hits in Europe)
"Where Are You Now?" by Jimmy Harnen w/ Synch
"Whirly Girl" by Oxo
"Whisper to a Scream (Birds Fly)" by Icicle Works
"White Horse" by Laid Back
"Who'll Be The Fool Tonight" by Larsen/Feiten Band
"Without Your Love" by Roger Daltrey (who is The Who's lead singer)
"Wondering Where the Lions Are" by Bruce Cockburn (who has several other hits in his native Canada)
"Yeah, Yeah, Yeah" by Judson Spence
"Yes, I'm Ready" by Teri DeSario (with K.C., the frontman of KC and the Sunshine Band)
"You Could Take My Heart Away" by Silver Condor
"You Don't Know" by Scarlett and Black
"You're a Friend of Mine" by Clarence Clemons (with Jackson Browne, who is not a one-hit wonder; Clemons was a member of Bruce Springsteen's E Street Band)
Poor Phillip...talk about taking notes...she said name "any"