Oh, this is a such a rich topic! I had to hit Wikipedia to make sure everything I liked was actually a one-hit wonder. It turns out that while I love Concrete Blonde for "Everybody Knows" they had a much more major hit called "Joey." (Yeah... once upon a time I actually knew that. I must be getting old.) Similarly, my favorite song by XTC is "Mayor of Simpleton" but they had a much larger hit called "Dear God" - but I remembered that before looking them up.
1) "Life in a Northern Town" by Dream Academy
2) "No Myth" by Michael Penn
3) "Wild Night" by Meshelle Ndegecello (featuring John Mellencamp)
4) "I'm Too Sexy" by Right Said Fred
5) "Take on Me" by A-ha
6) "99 Luft Balloons" by Nena
7) "Beds are Burning" by Midnight Oil
8) "Wicked Game" by Chris Isaak
9) "Jump Jive N Wail" by The Brian Setzer Orchestra
10) "One of Us" by Joan Osbourne
Now I want to go load up my iPod with 80s music!