Some random songs you never hear any more:
The Art of Noise - Paranoimia
Boston - Amanda
Berlin - Like Flames
Boy George - Everything I own (Once again, a cover, but I like it)
Bourgeious Tagg - Waiting for the World to Turn
Peter Cetera - Glory of Love
Cindy & The Saffrons - Past Present & Future
Company B - Fascinated
ELO - Calling America
ELO - Hold On Tight
Joe Fagin - Why don't we Spend the Night
Fairground Attraction - Perfect
Peter Gabriel - Sledgehammer (a classic, and not played enough IMO)
Billy Joel - A Matter of Trust
Laid Back - Sunshine Reggae
Alison Moyet - Is This Love
Billy Ocean - When the Going Gets Tough, The Tough Get Going
Pretty Poison - Catch Me I'm Falling
Pseudo Echo - Funky Town (Yes, I know it's not the original, but I like this one...

)
The Spectres - Teddy Bear
Underworld - Underneath The Radar
Kim Wilde - Cambodia
All stuff I really liked in the 80's, but seldom hear.
I'll think of more as the day goes by I'm sure.