Paul Nelson

abstract synth from Portland, Oregon.
Paul Nelson with "Labyrinth" from the album Vortex (1981):

Napalm Babies

"Don't Catch Me In the Blast" found on the White On Black (Experiments with Mass) cassette compilation (1982):

ed. 3/27/11: video embedding disabled, listen here: url: http://www.youtube.com/watch?v=1wJJzZt-2ZE

Sun Ra

anyone who has an affinity to the absurd, psychedelic, or metaphysical and hasn't yet heard of Sun Ra ought to do some immediate research. This is from 1956:

Pink Military

title track from Do Animals Believe In God? (1980):

Borghesia

early industrial music from what was then Yugoslavia.
"Discipline! (Punish Them)" from Surveillance and Punishment (1989):

Martin Dupont

"It's So" from Sleep Is A Luxury (1985)- fan video:

Clan of Xymox

the goth genre was born on the cusp of the new wave movement, birthed out of some of its darker acts, and was often referred to as dark or coldwave. Clan of Xymox was one of the first bands to be given the title.
here is their second single, "A Day" (1985):

Crash Course In Science

from Philadelphia, PA.
"Factory Forehead" from Signals From Pier 13 (1981):

Solid Space

another DIY tape release from early 80's UK, Solid Space with the album Space Museum (1982):
"Radio France"

"Destination Moon"

"Contemplation"

Barnes & Barnes

"Cemetery Girls" from Voobaha (1980):

"Linoleum" also from Voobaha:

Pas de Deux

"Cardiocleptomanie" from Axe Ends (1983):

The Moontrekkers

if you can believe it, this song was actually banned from UK radio upon release for being too scary. produced by Joe Meek, 1961:

Nico

after Chelsea Girl, Nico recorded three more albums with John Cale, consisting mostly of original compositions written and perfomed by Nico on her harmonium with Cale providing the backing instrumentation.
"My Only Child" and "All That Is My Own" from Desertshore (1970) as they appear in Philippe Garrel's film, La cicatrice interieure:

"König" didn't make it onto Desertshore but was also in the film:

Cleaners from Venus

Cleaners from Venus was a DIY cassette band formed in England in 1980 helmed by singer/songwriter Martin Newell, who has continued to produce an enormous amount of recordings to the present day.
"A Blue Wave" from the first Cleaners from Venus cassette, Blow Your Troubles Away (1981):

"This Rainy Day" from Midnight Cleaners (1982):

"Ghosts in Doorways" from In the Golden Autumn (1983):

Piero Piccioni

both from the film soundtrack to the Italian thriller Colpo Rovente:
"Red Hot" (1969)

"Colpo Rovente" (1969)