Suicide

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

"Cheree":

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):

Unknown DJ

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

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

Gandalf

american psych band, Gandalf with "Tiffany Rings" from their 1969 self-titled album:

William De Vaughn

diamond in the back, sun roof top, diggin' the scene with a gangster lean.
1974 single, "Be Thankful for What You've Got":

Afrika Bambaataa & the Soulsonic Force

Afrika Bambaataa & the Soulsonic Force were instrumental in the development of hip-hop (Afrika actually coined the term) and electro-funk with their unique blend of European electronic music, american funk, and rap. They helped push hip hop to the forefront of American dance music, and were one of the first hip hop groups to carry strong (and positive) political and social undertones.
"Looking for the Perfect Beat" video for the 1983 single:

"Planet Rock" from the 1982 Planet Patrol/Soul Sonic Force split EP:

"Renegades of Funk" video for the 1983 single:

Strawberry Alarm Clock

Though mostly considered to be a one-hit-wonder, Strawberry Alarm Clock released three albums from 1967-1968, during the height of the psychedelic movement in LA. They greatly influenced the early beginnings of LA bubblegum pop, which would grow to outlast and out-sell west coast psychedelia. The band broke apart in late '68, but released a 4th album, Good Morning Starshine, in '69 with an almost completely new line-up and a distinctly less psychedelic sound.
"Nightmare of Percussion" from their second album, Wake Up... It's Tomorrow (1968):

"Heated Love" from their 3rd album, The World in a Sea Shell (1968):

Devo

Before the hats came the glasses and yellow suits. Devo was formed sometime around 1973 at Kent State as a punk rock/art rock combo. They DIYed a few singles on their Booji Boy label, then were signed to Warner Bros. in '76. Here are some videos from a live performance in France in 1978, the year they released their first album, Q: Are We Not Men? A: We Are Devo.
"Gut Feeling/Slap Your Mammy" from Are We Not Men:

"Smart Patrol/Mr. DNA" from their second album, Duty for the Future (1979):

a devolved version of "Red Eye" also from Duty for the Future:

United States of America

Formed by electronic composer/musician Joseph Byrd at UCLA in 1967, United States of America artfully blended psychedelic sounds with chamber music, electronic experimentation, and avant-garde rock n roll. Their self titled LP (1968) was their only release.
The two songs I've selected showcase their soft rock meanderings mixed with mesmerizing tape and vocal effects and a calmer touch of psychedelia.
"Love Song for the Dead Che"

"Cloud Song"

Weather Report

for all you jazz-funk enthusiasts out there, Weather Report with "Teen Town" featuring the amazing Jaco Pastorius on bass!

The Short Wave Mystery

The only album ever released by the group was a four song EP of sorts called Pilots which was recorded while the members were in community college in California. 1000 copies were pressed, 500 of which were not even sold. the record, when for sale, can fetch up to $1000.
"Nice Girl":

"Ecaterina Szabo":

The Beach Boys

Before Brian Wilson retreated from the public eye in the late 60's, he and the rest of the Boys had been busy in the studio recording sessions for their new album, SMiLE (or Dumb Angel), which was intended to follow up Pet Sounds (1966). Wilson was pouring himself into writing songs for the album which he called "a teenage symphony to God," but for whatever reason, before the sessions could be mastered and arranged for release, Brian Wilson scrapped the entire project and left the band, taking most of the songs with him. Rumors state that Capitol Records and some of the other Beach Boys disliked the new direction Brian was taking the band, that Brian was addicted to LSD, and even that Brian was crushed after being shown a demo of "A Day in the Life" from Sgt. Pepper's Lonely Hearts Club Band and couldn't imagine ever topping it. Many of the songs from the SMiLE sessions were reworked by Capitol and released on subsequent albums, but the original '66-'67 sessions with Brian Wilson will remain unreleased until this year.
"Heroes and Villains"

"Wonderful"

"Cabinessence"

"Surf's Up"

That's Hot

someone's got a case of the mondays... me. This is a very self-indulgent post.
Early video art by G.G. Aries, music by Larry Gibbs, from California Images: Hi-Fi For the Eyes, 1983:

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:

Chrome

Helios Creed and Damon Edge with their third album, Half Machine Lip Moves (1979).
"Zombie Warfare"

"Mondo Anthem"

Claudine Longet

Claudine Longet with the "Nothing To Lose / White Horses" single from 1968.
Side A, "Nothing To Lose" was written by Henry Mancini and Donald black:

Side B, "White Horses" was written by Michael Carr and Ben Nisbet:

A Tribe Called Quest

"Electric Relaxation" from the 1993 album Midnight Marauders:

Lee Hazlewood & Ann Margaret

Lee and Ann perform "Chico" in 1968 on the Swedish TV special, "Love and Other Crimes"

Grandmaster Flash & The 4 MC's

mixtape of a live set from 1978 when hip hop was still a baby:

R. Stevie Moore

SIT DOWN. performing on the Uncle Floyd Show, NJ, 1980: