I can recommend "The American Fiddle Method", a new series by Brian Wicklund. It's a great introduction to folk/trad fiddling, and it starts out with well-known tunes and advances quickly. Not all the tunes he teaches are American. For example, one of the beginning tunes is the Arran Boat Song. I started playing fiddle with this method (it's a Book-and-CD series with two volumes, plus an optional DVD) only this summer, and I'm already playing dozens of tunes and even writing some of my own.
SmokinBill@aol.com
PS you can hear me playing one of the tunes from the series, Angelina Baker, on my Web site: