I'd learn the viola d'amore just to say I play the viola of love
anybody likes tuba..?
I also love the ukelele, has anyone heard of Jake Shimabukuro? He's just fantastic.
I couldn't imagine going through life without being able to hear an accordian.
A recent favorite of mine is the mighty Warr Guitar, a 8-12 string two-hand tapping instrument that is often used as a bass instrument, since it's range covers that of a 5-string bass and guitar combined. Trey Gunn uses one of these in King Crimson. Listen to how awesome it is on this song's intro:&feature=related