I love falling asleep to chill music. This thread is for such music, if you don't particularly fall asleep to it, but it's got that vibe, that works too.
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Micking Birds - 'The Loop'. I really like the hook at around 2:45, but it's only used occasionally. Otherwise, the name of the song is a good description of it, as it is mostly just a looped guitar riff and otherwise ambient noise.
Fredrik - 'Black Fur'. One of my favorite bands as of recently. Swedish band, a lot of their stuff reminds me of a catchier/better Sigur Ros.
Horse Feathers - 'Falling Through The Roof'. Folksy Acoustic music. Possibly not up everyone's alley, but I like them.