I'd like to turn it round and ask what instruments can't be played without any musical training. I was playing tunes on the recorder by ear before I ever learned to read dots; I can still pick out a tune by ear as quickly as I can sight-read (i.e. not very quickly). My Dad used to play piano, and he never learned to read dots (although he could sight-read solfa). How he learned the left-hand parts I'll never know. I find the idea of being a self-taught guitarist equally mindboggling, but people do do it - one of the best guitarists I know plays chords with names like "D with an extra bit".

So what instrument is there that's so complex and counter-intuitive that no untaught outsider could ever learn to find their way around it? Lute? Pipe organ? Bandoneon?