One that I haven't got very far with yet (bought a few months ago): the Turkish tanbur - long-necked microtonally fretted baritone banjo, for a couple of centuries the standard lead instrument for Turkish classical music. Here's one of the best living players:

Murat Aydemir: Ussak taksim

The technique is like nothing I've ever played before - melodies pretty much stay on one course and you're up and down that immensely long neck.

According to Evliya Celebi, writing in the 17th century, it was the standard instrument of Sodom and Gomorrah. He played it himself and seems to have started the tradition of banjo jokes.