I'll admit to being one of those who didn't know her until her formal debut with Born to Die but having listened to a couple of songs I have to say her voice is very, very beautiful. Some of my favourites (and less popular, unfortunately) songs below.
Mermaid Motel has this silky, smoky eroticism to it that's ridiculously infectious. Put Me In A Movie is a really cutting, honest song. I love the softness of her voice in that one. Same can be said for Oh Say Can You See, though it's very much more powerful. The line, "A voice from Nirvana says, 'Come as you are.'"