A few other possibilities (in no particular order):
Mum
Coil
Black Sun Productions
Psychic TV (their deep lounge stuff, anyway)
Banco de Gaia
Acid Mothers Temple (much of their stuff is mellow, though much is gonzo spacerock)
Kawabata Makoto (a member of AMT)
Anubian Lights
The Transmissionary Six
Chris & Cosey (aka CTI)
Sheila Chandra (her stuff is very dated, though)
Transglobal Underground
Saeta (very reminiscent of This Mortal Coil)
Spiral Realms
Cheb I Sabbah
Midival Punditz
The Brain
Heather Duby (electro-chanteuse…stick to her first and third albums)
Vas
Zero Gravity
Transjoik
Some great suggestions in this thread.
If you like Spiritualized (one of my alltime faves), don’t forget all the other “prog pop” out there, like Jeff Buckley, Flaming Lips, Mercury Rev, et al.
I have a lot of music under my “chill” genre in my iPod, but I don’t have it with me, so top of my head . . .
Nightmares on Wax “Smoker’s Delight”
9 Lazy 9
Nobukazu Takemura
Holly Cole’s “Temptation”
Rickie Lee Jones “Ghostyhead”
Astrud Gilberto
Walter Wanderly
DJ Krush
Red Snapper
Prefuse 73
Psyco on da Bus
Jimi Tenor
Fridge
Four Tet
. . . all I can squeeze from my brain right now. Will add more later when I have my pod.
Hey, I thought about them after posting yesterday because I was listening to the song “no more mosquitoes” which would definitely fit. I only know a couple songs by them, though (the others are a instrumental cover of Iron Man and a remix they worked on for Breathe Me by Sia) so I didn’t know if that song is representive of their normal style.
Possibly the oddest band/bunch of loons to ever walk the Earth. I read an interview a month or two ago with Genesis and his wife and their project to have plastic surgery in order to look exactly like each other is nearing its conclusion by the looks of things. Godstar, indeed 
I can’t find clips for some of the recommendations, but of those I can I’ve ordered the following:
Details - Frou Frou
Give Up - Postal Service
Karma - Delerium
Lost Horizon - Lemon Jelly (I don’t know why I don’t have this already - I think I may have got them mixed up with the that “Billy goats gruff” lot
I’m also going to get some others when I’ve got Christmas finished with.
I’d also like to thank the posters who reminded me of stuff I’ve already got:
Fischerspooner
Zero 7
Mogwai
Nightmares on Wax
If anyone’s still reading who has a lot of Four Tet stuff- what do you recommend? There’s a load of stuff available?
Einsturzende Neubaten is a German percussion group I got turned on to by a really insane ex; they’re amazing in concert and cd.