I use ambient music a LOT in worship and learning settings, and have acquired a bunch of music over the past few years thanks to the recommendations of a number of friends and my own exploring. Here are some great musicians to start with. The styles vary from no beat to more upbeat, from fluid to more jarring, but all excellent.
Album links are to the Australian iTunes where available (or alternatively Amazon or some other band site). If you're in another country, you should be redirected to the relevant iTunes store for your country.
Quite a few of these came from emusic.com where I have a monthly subscription, so they're relatively inexpensive. Sadly, emusic doesnt currently accept new Australians subs due to local recording company agreements.
Eraldo Bernocchi & Harold Budd - Music for "Fragments From The Inside"
Jon Birch and Johnny Baker - generally laid-back beats (go for the instrumental albums, although the others are worth hearing too) - at Proost
Harold Budd - Agua
Cluster - "Qua"
Dawn Landes - Dawn's Music
Efterklang - "Tripper"
John Foxx & Harold Budd - Translucence / Drift Music
Goldmund - "Corduroy Road", "The Malady of Elegance", "Two Point Discrimination"
Hauschka - "Room to Expand"
Hauschka and Hildur Guonadottir - "Pan Tone"
Helios - Eingya
Hilmar Om Hilmarrson & Sigur Ros - "Angels of the Universe"
Jonsi and Alex - "Riceboy Sleeps"
Labradford - "fixed:content"
Clint Mansell has some great soundtrack stuff, for example "Moon"
Brian McBride - "The Effective Disconnect"
Moby - "Hotel" B-Sides bonus CD (and bits of his other work), "Ambient"
Nils Frahm - plenty of excellent music. check out the albums "The Bells", "Felt", "Screws", "Spaces"
Olafur Arnalds -""and they have escaped the weight of darkness", "For Now I Am Winter", "Living Room Songs", Re:Member",
Olafur Arnalds with Nils Fram) - "Trance Frendz"
Oneida - "Oneida", "A List of the Burning Mountains" (disturbing soundtrack stuff)
Duane Pitre - "Free"
Nick Cave and Warren Ellis do amazing soundtracks - "White Lunar" is a collection fo pieces, also "The Assassination Of Jesse James By The Coward Robert Ford", "Loin des Hommes"
Jon Hopkins - "Opalescent" - most of his work is a bit too "busy" but there are some lovely slower pieces
I also collect movie soundtracks as they are full of wonderful mood pieces.
There is more stuff but its harder to get... and there are loads of individual songs from particular albums that aren't listed here. and some albums that would melt your brain unless you had a particularly quirky use for a particular song.
Hope this helps you.