Sweet Jane
I'm trying to recall when I first heard the Cowboy Junkies, and I'm going to have to go with when I saw the creepy, disturbing, and utterly fantastic Natural Born Killers (has it really been 15 years??) back in 1994. You can hear this song, originally done by The Velvet Underground, during Mallory's poem recital to Mickey in the desert in an early scene. In fact, the entire soundtrack is perfectly selected, not to mention diverse, and does a fantastic job of creating just the right mood for every surreal moment.
After hearing the song, I immediately headed over to my local Karma record store and purchased the Junkies' Trinity Session. This is easily the most mellow album in my entire collection, and I listen to it on auto-repeat on days meant for chilling. Or sleeping.
