Tom Waits...well, what can you say, the man is a musical genius! A favorite album would be difficult, but if pressed for a desert island disk I'd say Swordfishtrombone. His new ones are wonderful too.
Tori Amos is also a longtime favorite. If you get a chance to see her perform in a good acoustical setting, RUN don't walk to see her play those keyboards and belt out that wonderful poetry! Boys for Pele is a great album!
I just recently saw Patty Griffin in concert and just can't stop listening to two of her three albums. 1000 kisses is probably my favorite and her most recent.
These latter two have a kind of folksy, even country twang to them, so that really rubs you the wrong way, well..your loss.
Gillian Welch, also puts on a brilliant show. Her partner, David Rawlings, is just an amazing guitar player. Her stuff is pretty somber and beautiful, so you've got to be in the mood, but I do love her music.
There are other performers who I do love to listen to, like Eva Cassidy, Holly Cole, Jacintha, Patricia Barber...but many of the tunes these gifted women do sing are covers. Their originals are good too, but when you talk about long-term staying power, I do like the originality of the ones I listed at the top. Good thread.