Among my dulcimer friends, "Cherokee Shuffle" was the tune that marked your rise to the level of Really Good Player. It's actually not too bad to learn but it sounds like a million bucks once you have it down.

My all-time favorite was the guy who performed at Glen Rose (home of the Texas state dulcimer championships) in, I think it was 1997, and played the William Tell Overture--the whole thing, not just the Lone Ranger famous part--by bouncing a pencil on the strings.