In continuing with the "why haven't we already posted this" theme, I bring you Fiona Apple.
This song, an early single, set Ms. Apple up for greater airplay success to come, earning heavy rotation on MTV, when they still occasionally played videos. The tune is bassline-heavy, with a compelling piano/guitar arrangement - she is a pianist first. Combine that musical dark dream state with her husky voice and the fact that she looks a LOT younger than she actually is, and you've got a hit on your hands!
Really, in the US, Fiona Apple is a one hit wonder. And because I'm a populist and pander to the wants of the people, here is her biggest hit. In all seriousness, it is an excellent song that deserved every bit of airplay it received (and the Grammy she earned for the performance). It's a little lighter-hearted in sound, but equals "Sleep To Dream" in darkness of theme.
Update: I was reminded that we DID feature Fiona Apple on Totally Covered, with her Beatles cover. Another great song.