Suicide

Alan Vega and Martin Rev from NYC, their first album from 1977, Suicide.
"Rocket USA":

"Cheree":

Amon Düül II

Amon Düül II was one of the most influential krautrock conglomerations, with members constantly flowing in and out and branching into other groups and new musical territory. This particular period, around the release of Yeti (1970), turned out to be a seminal moment in the history of the group, marking the beginning of their underground success outside of Germany. The album shows a remarkable breadth of expression, from strange, trance-like moments of noise, constrained acoustic ragas and improvisations, to explosive, dirty, electric prog with slamming beats and tape effects.
"Archangel Thunderbird":

"Pale Gallery":

"Hallucination Guillotine":

Tyndall

Nik Tyndall and Rudolf Langer with their 3rd LP, Reflexionen (1982).
"Strassen Der Nacht":

Human League

the Human League from later in their career with their 1986 single, "Human":

Angelo Badalamenti

Angelo Badalamenti recorded the scores for several of David Lynch's films.
"Twin Peaks Theme", as it appears in the opening segment of the pilot episode of David Lynch's Twin Peaks:

"Fred's World" from the Lost Highway soundtrack (1997):

"Mysteries of Love" as it appears in Blue Velvet (1987):

Billy Idol

if the 1980's had just one douche bag to call it's own, it would be Billy Idol. here he is showing his less "hard" side with two of his most popular ballads.
"Eyes Without A Face" from Rebel Yell (1983):

"Sweet Sixteen" from Whiplash Smile (1986):

Unknown DJ

Andre Manuel, the Unknown DJ, early west-coast electro beats.
"Basstronic" single, 1988:

better audio: http://youtu.be/ytddqtWSP-E