This should cover a bunch of different Ambient styles, but all of the artists are absolutely fantastic and worth digging into. I'm definitely leaving out a fuckload more, but there are a ton of great suggestions in the other responses, too. Happy listening! :D
Biosphere
Ryuichi Sakamoto
Loscil
A Strangely Isolated Place (record label & mix series)
Silent Season (record label)
Kelly Moran
Rafael Anton Irisarri
Harold Budd
Steve Roach
Terre Thaemlitz
Gel-Sol
Koss
Nils Frahm
FAX Records
Pete Namlook
Hiroshi Yoshimura
Benoit Pioulard
Carlos Nino
Woob (particularly woob1194)
ASC
Autumn of Communion
Wanderwelle
Celer
Christina Vantzou
Julianna Barwick
Mary Lattimore
Grouper
Suzanne Ciani
MPU101
Deru
Lusine (Language Barrier in particular, his only full-Ambient album)
Nice list. I would second Ryuichi Sakamoto, Loscil, Julianna Barwick, Mary Lattimore, and Grouper for sure and there are lots of other good ones on there.
I'd add Windy & Carl, A Winged Victory for the Sullen, Yui Odonera (lots from the Serein label actually), Max Richter, and most of all Stars of the Lid.
The Disintegration Loops is lovely and I found it very thought-provoking. The concept of hearing the medium being destroyed, in this sort of breathing / heartbeat / day and night cycle, is a very powerful way to think about mortality.
One of the tracks still sounds like you're hearing someone drowning over the course of 17 minutes and it's terrifying. It's the first track here, though I believe they are named / ordered incorrectly. Just comparing 2 minutes in vs 15 minutes.. it still creeps me out.
It's every Sunday early morning Pacific time but you can listen to recent shows in their streaming archive. The whole show is modern ambient and similar music, it's absolutely fantastic and a great way to hear new artists in the genre.
edit: lol someone already posted it. This should give you an idea of how good this show is if multiple people are suggesting it. I've never heard any other show/podcast/or anything as comprehensive about new ambient music as this one.
It's fantastic. I also really enjoy the blues show the immediately follows it, Preachin' the Blues. Bit of a contrast but the curation on both shows is stellar.
I'd look into stuff like Harold Budd, William Basinski, or Jon Hassell (who in turn influenced Eno; you can hear some similarities but also radical differences because Hassell played processed trumpet and had a much more dense sound palette. Albums like "Fascinoma" or "The Surgeon of the Night Sky Restores Dead Things By he Power of Sound" for starters, but they did one album together in the early 80s called "Possible Musics" worth a listen)
There is a label called Past Inside the Present that does a lot of landscape/soundscape/dreamscape recordings. They are on bandcamp and https://www.pastinsidethepresent.com/ (I am not affiliated, I just have a fair number of their recordings). Check out Zake (I think he is the owner too) and also 36.
I'll throw in the 'Ghosts' series by Nine Inch Nails. These land somewhere between Eno and Aphex Twin and were basically a precursor to Trent Reznor and Atticus Ross's soundtrack work (some of which may also be worth a listen).
I absolutely love "Music for REAL Airports" by The Black Dog.
An obvious poke at the original, it features a darker, moody and slightly unsettling ambience, with some minimal percussive elements in a couple of tracks. It's meant to remind you of the real experience of being in an airport, which isn't exactly a pleasant experience :)
The band The Glitch Mob maintain an ambient playlist on spotify that I listen to constantly while working. They update it really regularly (4 day since last song added right now).
Music for Programming[0] is a nice site with mixes of music, most of it ambient, intended to provide focus while programming. Each mix has a setlist so you can follow along and perhaps find some new artists to explore.
Steve Reich did a number of pieces that are loopy and programatic in the 1960's and 70's, but with analog instruments. Kind of like Javanese Gamelan but more western style.
Music for 18 Musicians
The Desert Music
Drumming
I think it is debatable if they are "ambient", since some get quite loud, but they are meditative.
If you like Robin Guthrie, you may like the ambient music of Harold Budd, one of his collaborators. One of the their cool joint projects is the instrumental score for the film Mysterious Skin from 2004.
I didn't find him from the mentions yet so I'll add Gas. Start with Zauberberg, Königsforst and Pop, and if you like them get completely lost with the rest of his productions.
Some of my favorites include Stars of the Lid, Eluvium, Robin Guthrie (So Many Short Years Ago), Brian McBride (Overture for other halfs), and Helios.