Ambient favorites

Brian Eno "Music for Airports"
Philip Glass and Uakti "Aguas da Amazonias" (best of all.. IMO)
Enya "Watermark"
Movie soundtrack "Run Lola Run"
Bach "Goldberg variations"
Nearly anything on the Windham Hill label...
These are a few I like, which I can think of off the top of my head.
They may not exactly 'fit' the definition, but they are in the same way...

I've always been an Eno fan, but in the past 2 years have really expanded my Ambient catalog. Some of my favorite artists:

Eno - he has a lot out - everything in his catalog is worth having and most is even better than "Music for Airports"

Harold Budd - like everything I have by him
Frip and Eno - especially "Evening Star"
Michael Brook
John Foxx
Robin Guthrie - not totally ambient - some is a little more lively.
Klaus Schulze - more electronic, but ambient
Tangerine Dream - really more electronic, less ambient

Also - some Jazz "ambient" I like a lot:

Tord Gustavsen Trio - all of their catalog
Bobo Stenson Trio - Cantando, War Orphans
Ralph Towner and Gay Burton - "Matchbook"

Here are some mixes I have on 8tracks.com:

Introduction to Pete Namlook & Fax Records
http://8tracks.com/synthfreek/synthfreek-s-introduction-to-fax-records-pete-namlook

ECM Records Mix for fans of electronic/ambient music
http://8tracks.com/synthfreek/synthfreek-s-intro-to-ecm-records-mix-for-electronic-music-listeners

Deep Ambient Pt. 1
http://8tracks.com/synthfreek/synthfreek-s-deeper-than-deep-ambient-mix-part-1

Deep Ambient Pt. 2
http://8tracks.com/synthfreek/synthfreek-s-deeper-than-deep-ambient-mix-part-2

Ambient Dub Techno
http://8tracks.com/synthfreek/synthfreek-s-ambient-dub-techno-mix

Some Mid-90s Chilout
http://8tracks.com/synthfreek/some-mid90s-chillout-classics

Boards of Canada "Music Has a Right to Children" & "Geogaddi"
Aphex Twin "Selected Ambient Works 85-92" & "Selected Ambient Works Vol. II"
Future Sound of London "Lifeform"
Nicolas Jaar "Space is Only Noise"

Check out http://www.ambientmusicgude.com for more suggestions.