What are some good songs that are nice and soothing, good to drift off with? And I don’t mean insipid music like muzak, just songs you deem to be nice and sleepish. Thanks. 
Dire Straits Brothers in arms can take you away, you might wake up during the third to last song.
Vivaldi’s guitar concerto in G is good
There is a couple of pieces from Cosmos one with a French name and another calledFly night Bird I think.
Sorry I can’t remembr those titles exactly, hope others can help
Enya’s Watermark puts me to sleep every time. I’ve never made it all the way through the CD in one listen.
I don’t think I’ve ever made it through all of Radiohead’s Kid A. Guaranteed to put you to sleep or your money back!
On long car trips I usually pipe Hybrid Theory (Linkin Park) through my headphones and fall asleep… though I think it’s more conditioning than anything else 
Pachabel’s Canon in D on repeat also does it for me.
Hmm…I don’t necessarily mean songs that actually aid you in sleeping, but more ones that well complement a sleepy, relaxed mood.
Daniel Lanois’ new album Shine is pretty good if you’re in a sleepy mood. It’s full of soft, beautiful atmospheres, and half of it is instrumental.
Bjork - “my headphones”
The Orb’s “Adventures Beyond the Ultraworld” is some of the most relaxing stuff I know of. Even when you’re, er, sober, to put it legally.
Not me! I always find that if I put it on late at night, How to Disappear Completely and Treefingers will put me in a beautiful trance before I’m rudely jerked back to the world of the awake by the opening riff of Optimistic. It’s the musical equivalent of a bucket of cold water being tipped over your head.
You will not be able to stay awake through this.The Pachabel’s Canon with Ocean Sounds But I think that’s what they intended.
Brian Eno’s Music for Airports.
I made a tape of The Doors’ Riders on the Storm and followed it with a recording of a thunderstorm. Love it!
When I was in college my roommate used to play Rachmaninoff’s Second Piano Concerto each night as we were drifting off. After she left, I had to go out and buy the piece so that I could get some sleep again.
I always put on something like “Pure Moods” or “The Essential World Disc 1999” which oddly enough you can purchase here now.
The Tindersticks’ self-titled album, and their greatest hits compilation Donkeys. Think somewhere between Leonard Cohen and Nick Cave, but British, heavy on strings and with a nasty sense of humour that cuts through the gloom.
I did not realize that “Pure Moods” was so hard to find, so here’s a link to the album I mean. There are sound samples on both the links I provided.
Bah! Why can’t I get the link to work? 
Copying and pasting it seems to work, so here goes.
Aha! I see, I’ll turn off smilies, and see if that works. blush Fixed link at last?
I usually fall asleep to any of the following:
Chopin’s nocturnes (op. 9 no. 1 and no. 2 being my favorites)
Neu! - Neu! or Neu! 75
Tortoise - Millions Living Now Will Never Die
Massive Attack -Mezzanine
Stereolab - Mars Audiac Quintet
Anima Sound System - Hungarian Astronaut
Actually, a lot of these have a fairly pulsing beat, and some can get a bit rockin’, but I find that for me, these have the right effect, but YMMV. The last one is a bit obscure, but is available in the West…quite minimalist, folk-influence, dub/drum-and-bass sort of thing.
My top, number one of all time go-to-sleep-in-a-pleasant-mood music would be the Boards of Canada album Music Has the Right to Children. Lovely stuff.
I find the Depeche Mode album Violator works a treat as well.