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):

Lush

as shoegaze and dreampop were just beginning to bubble up in the UK in the late 80's, Lush signed with 4AD and began a slow rise through the underground circuit, garnering plenty of credentials along the way. fans praise Lush for their consistency through the years. here's a glorious VHS video of the 1991 single De-Luxe from early in their career:

Further

Further was an LA group from the early 90's who's influence is muted at best (especially in light of the current music trends coming from the area) despite the fact that members of the group have deep rooted connections with modern genre benders and trend setters such as Beachwood Sparks and Ariel Pink's Haunted Graffiti. The following songs are from Further's 3rd and 4th album releases, Grimes Golden and Sometimes Chimes, both from 1994.
"California Bummer" from Grimes Golden:

"Quiet Riot Grrrl" from Grimes Golden:

"Surfing Pointers" from Sometimes Chimes:

A Tribe Called Quest

"Electric Relaxation" from the 1993 album Midnight Marauders:

Black Sheep

"Without A Doubt" from Non-Fiction (1994):

Lonnie Liston Smith

"Colors of the Rainbow" from Watercolors (1991):

Roger Troutman

"Emotions" from Bridging the Gap (1991):

A Tribe Called Quest

from the album Low End Theory (1991), "Jazz (We've Got)" and "Buggin' Out":

Alan Parsons

From his solo album, On Air (1996):
"Cloudbreak"

Helios Creed

Helios Creed was a member of Chrome along with Damon Edge in the late '70's-early '80s, and with the dissolution of Chrome he went on to record several solo records. from the album NUGG the Transport (1996):

The Cocteau Twins

"Essence" from Four-Calendar Cafe (1993)
"Oomingmak" from the album Victorialand (1986)

Magnetic Fields

The following songs appeared on the album Holiday (1994). Songs by Stephin Merritt.
Strange Powers

All You Ever Do Is Walk Away

Eric B. and Rakim

"In the Ghetto" from 1990's Let the Rythm Hit 'Em.

Medusa

the emcee goddess, Medusa with "power to the P," underground hip hop from early 1990's Los Angeles.

The Pharcyde

1993 single "4 Better Or 4 Worse." thanks to Lamaraba for turning me on to this.

Cabaret Voltaire

cabaret voltaire was one of the early avant-garde electronic groups of the british new wave, playing alongside bands like joy division, throbbing gristle, gary numan, and the human league as they stepped into the limelight. Cab kept their heads low all through the synthpop era, constantly releasing a slew of underground material and pushing the envelope for electronic music. in the late 70s, their use of tape samples and home made loops put them at the forefront of what was then the cutting edge of electronic music and now known to be far ahead of its time. through the years they've managed to keep quite a dedicated following; their 17th full length album was just released this may, 2010.
the following are a few selections from a series of videos recorded in 1990 promoting the album Groovy, Laidback and Nasty (follow the links below to see more).

rescue me (1990/96) from Nick Cope on Vimeo.

Easy Life (1990/96) from Nick Cope on Vimeo.

Magic from Nick Cope on Vimeo.

Meantraitors

in honor of my tooth extraction this morning;
russian acoustic punk?

Lionel Davis

after seeing this video, i was immediately impressed by how bad it was, but after digging around on the net for a while, i still don't really know much about mr. lionel davis. his cd, the electric man, is for sale on amazon.com and includes the track below, as well as other sordid hits like "big breast obsessed."

Alice Coltrane

filmed for BBC, 1992