"Peach, Plum, Pear" - Joanna Newsom. Live in 2004.
Newsom's performances on harp, piano, and harpsichord won me over immediately. The accompaniment makes great use of layered rhythms unlike anything in popular music outside of more adventurous funk. Her songs are as much reminiscent of Philip Glass and other minimalist composers as the African kora music Newsom sites as an influence.
In contrast, her voice had to grow on me, as seems to be the case for most fans. She's toned down the squeak in her voice on her latest album and live, but I can still see how giving her a chance takes the same sort of leap that listeners have to take with Tom Waits, Shane MacGowan, and Billie Holiday. (I chose the live version above rather than the official video in part because the live version does not feature the bizarre overdubs of the album version.)
I chose her this week because among the "New Weird Americ"a/"Freak Folk" scene Newsom stands out has having both a debt to traditional/folk music and a unique vision. Her pairing with Van Dyke Parks on Ys is natural and obvious. Whereas the 60s counter-culture adoption of folk music more or less updated old blues and country with a hip but musically uninteresting rock beat, Parks actually used the vocabulary of traditional Americana to express new musical ideas without "dumbing down" the music by placing it over a steady four rock rhythm. In the same way, while many other current folk rock bands simply play folk with an updated indie aesthetic, Newsom appears to be on the verge of creating something truly wonderful and new. Where others pile layers of traditional instruments on top of a guitar-bass-drum arrangement, Newsom works her magic into the melody and rhythm of the song itself.
If you want to read more, here's an interview from 2006 and another more recent one.