Usually, I listen to more electronic, soothing music as my "chillout" music, especially Sigur Ros, The Album Leaf, and A Silver Mt. Zion. Other times, I listen to Belle and Sebastian, The Beatles, and The Decemberists. I suppose it's all about how I feel at the time.
Over The Rhine, The Decemberists, Death Cab for Cutie and Pink Martini are some of my favorites. I can't emphasize the incredible talent of Over The Rhine enough, they are the biggest thing in independent music in my opinion.
Cinephile - What becomes of us was featured in an episode of CSI and the internet exploded (CSI circles) with trying to get this song...eventually the band released their EP onto the net (which i got) and its about 75% cool chilled Songs..
Nightmares on Wax - Les Nuits is an excellent one
Air - la femme d'argent is one of my all timers
Hooverphonic are cool
Zero 7 are another (esp Destiny and In the Waiting Line are good)