Er, Tears for Fears wasn't quite a one-hit-wonder. There was Change, Mad World, Pale Shelter, Suffer the Children, Shout, Mad World, and Everybody Wants to Rule the World (crap, that one). Change was one of the best dance songs of 1983, and Pale Shelter one of the most beautiful.
I played "The Hurting" to death – until I hated it. It was a great album.
As for others, my list was a lot like Chorita's, at least by the mid/late-eighties. Before that, I guess King Crimson's Discipline wasn't on too many playlists…
But a few more no one has mentioned:
The One Thing - INXS
She Blinded Me with Science - Thomas Dolby
Living on the Ceiling - Blancmange
Burning Down the House - Talking Heads
Bloody Sunday - U2
Birthday - The Sugarcubes
Joey - Concrete Blonde (technically it's 1990, but who's counting…)
The Dogs of War - Pink Floyd
Can't Hardly Wait - The Replacements (not their best, but the only one that made it radio, I think)