These were not all hits, but they were all released in the 80s and are interesting (I think!). A few are from slightly obscure bands that may be hard to find, but most are not.
"She Sells Sanctuary" by The Cult
"Love Removal Machine" by The Cult
"Please Don’t Touch" by Motorhead & Girlschool
"Better Be Home Soon" by Crowded House
"E = MC2" by Big Audio Dynamite
"Misguided Angel" by Cowboy Junkies
"Real Gone Kid" by Deacon Blue
"Hymn To Her" by The Pretenders
"Rise" by Public Image Limited
"Wishful Thinking" by China Crisis
"Makes No Sense At All" by Husker Du
"Killermont Street" by Aztec Camera
"Just What I Needed" by The Cars
"Ca Plane Pour Moi" by Plastic Bertrand (there is a great Sonic Youth cover of it, too.)
"She's Leaving" by OMD
"Vive Le Rock" by Adam Ant
"True Faith" by New Order
"Freeze Frame" by J Geils Band
"Going Underground" by The Jam
"Under Pressure" by Queen & David Bowie
"When Love Breaks Down" by Prefab Sprout
"Live It Up" by Mental As Anything
"Special Brew" by Bad Manners
"Happy Hour" by The Housemartins
"Primary" by The Cure
"Jericho" by Simply Red
"Radio Radio" by Elvis Costello
"New England" by Kristy MacColl
"Senses Working Overtime" by XTC
"Too Much Too Young' by The Specials
"Tide Is High" by Blondie
"Souvenir" by OMD
"Forever Live And Die" by OMD
"Mongoloid" by Devo
"Rock Lobster" by The B-52s
"The Sound Of The Crowd" by Human League
"Open Your Heart" by Human League
"Darkness" by Human League
"I Don't Like Mondays" by The Boomtown Rats
"Stop" by Sam Brown
"Love Will Tear Us Apart" by Joy Division
"Our Lips Are Sealed" by The Go-Go's
"I Melt With You" by Modern English (always wrongly attributed to The Cure or someone else - it is not a Cure song, it just gets labelled that way on P2P downloads, LOL!)
"Alphabet Street" by Prince
"Police On My Back" by The Clash
"Happy When It Rains" by The Jesus & Mary Chain
"As Yet Untitled" by Terence Trent D'Arby
"The Unforgettable Fire" by U2
"Bela Lugosi's Dead" by Bauhaus
"Hold On Tight" by ELO
"Life In A Northern Town" by Dream Academy
"A Church Not Made With Hands" by The Waterboys
"About You" by The Jesus & Mary Chain
"What You're Proposing" by Status Quo
"Fade To Grey" by Visage
"Keep On Keepin' On" by The Redskins
"It Can Be Done" by The Redskins
"Wise Up! Sucker" by Pop Will Eat Itself
"Can U Dig It?" by Pop Will Eat Itself
"Cath" by The Bluebells
"It's Tricky" by Run DMC
"Purple Rain" by Prince
"Religion" by Elton John
"Mary's Prayer" by Danny Wilson
"Another Nail In My Heart" by Squeeze
"Electric Dreams" by Giorgio Moroder
"Turning Japanese" by The Vapors
"Geno" by Dexy's Midnight Runners
"Oliver's Army" by Elvis Costello
"Doors Of Your Heart" by The Beat
"The Bitterest Pill" by The Jam
"White Lines" by Grandmaster Flash