So many great bands listed here. I was gonna start quoting people but it just got overwhelming.
Dyna Mo's gonna make me break out my Aldo Nova shirt.
A few I'll add-
Adam Ant
Talking Heads
Psychadelic Furs
Tangerine Dream
Shreikback
Gang of Four
Echo and the Bunnymen
Stray Cats
Killing Joke
The Church
It's hard, there are alot of bands that I like from that era that kind of straddle the decades, like the Clash mentioned above, also The Stranglers, Wreckless Eric, etc.
So many good bands, hard to know where to start, but that's what comes off the top of my head.
Also Big Country by Big Country is one of my favorite songs ever and I don't know why.
http://www.dailymotion.com/video/x10...-country_music