Fishelle, I bow in your direction. Jesca Hoop is freaking brilliant, and deserves to be as well-known as Waits.
There are few artists whose entire catalog I will recommend, but here are a couple of disks I unreservedly adore:
Melody Gardot's "Worrisome Heart." One of my great hopes is to hear Gardot cover Hoop.
Sam Baker's "Mercy." This man was severely, severely damaged, and has come back from it.
And for sheer fun, Richard Thompson's "1,000 Years of Popular Music." Thompson selects and performs his favorites from the last 1,000 years. Just plain fun. Listen carefully for the exit music at the end; it's a madrigal arrangement of something much more recent. If you can read Chaucer in the original Middle English, the title gives you a big clue: "Marry, Ageyn Hic Hev Donne Yt."
I've thought long and hard at what to post on this thread and I'm going to limit myself to one artist.
His lyrics inspired me to start writing. His production work redefined hip-hop. He's never let himself be defined by the fact he is a 'white rapper' - that shit is irrelevent to him and to his fans. He has a Dylan-esque ability to nail complex concepts with a couplet. His sonic pallette brings back the explosions, air-horns, sirens and screams of urban New York to a hip-hop scene that has embraced gentrification and the nouveau-riche. He's angry like Chuck D, and as horror as Tyler, and more consistent than either. Ladies and gentlemen, YOU MUST LISTEN to... El-P.
This guys are one of those bands that I discovered long after they were done and gone, and went "how the HELL did I not hear about these guys when they were big!" Angry, growly pop jazz for the Nirvana era.