The 2004 self-released album Unbelonging by Danish one-man project Mushi (though it was actually called Mushy back then). The list of influences is quite an interesting read and includes just about everything (and everyone) from Cabaret (genre) over Calexico to The Pixies. And it is indeed rather difficult fitting the music of Mushi into any specific category, but no matter what genres are being added to the mix, the fine melody lines are always present underneath it all, which makes listening to the album a pleasant and highly entertaining experience. And of course I should mention that the entire album is available for free right here.
+ Grease Monkey
+ Elise And The Guardian Angel
+ The Nightcrawler
A new album called Unfairytales was released last month, but no songs are currently available for free (but five new and really good ones can be streamed here). I'll get back to that album, if/whenever a track (or two) can be legally shared.