Paul Warren - Listen To The Mockingbird (buy)
Kessinger Brothers - Turkey In The Straw (buy)
Johnny Gimble - Ragtime Annie (buy)
Bonus track : Quinteto Tipico Mexicano - Sobre las olas (Over The Waves) (buy)
(My main source for this post is Bill C. Malone's Country Music, USA)
Some fiddle tunes, among the most popular, didn't come directly from the folk repertory, but were composed and sometimes sold as sheet music during the 19th century.
Some came from black-face minstrelsy, like "Old Dan Tucker", "Turkey in the Straw" ( a song dating from the 1820s and originally called "Old Zip Coon"), "Cotton Eyed Joe" or "Listen to the Mockingbird", which became a classic for fiddle virtuosos and entertainers who could imitate various species of birds with their instrument (like bluegrass musician Paul Warren in the first track).
Other tunes came from the various popular styles : "Arkansas Traveler"was composed in the 1800s; "Ragtime Annie", here played by Texas fiddler and one time -Bob Wills sideman Johnny Gimble, but also "Dill Pickle Rag" or "Chicken Reel" were adaptations of popular dances.
And there were those which came for foreign countries. As Malone says, "If the country fiddler heard a good tune, he made it his own, whether it came from his own immediate experience, was a legacy from his ancestors, or moved into his consciousness from a foreign source. "Over the Waves", which is still probably the most popular country waltz, was originally written as "Sobre las olas" by the Mexican composer Juventino Rosas."
As a Mexican music fan, I couldn't resist to add as a bonus track a Mexican version of this classic.
Another foreign tune turned into a fiddle standard is "Under The Double Eagle", originally a patriotic march by the Austrian composer Josef Wagner which became a favorite of John Philip Sousa and thus made its way into American music.