In Ireland there are Set Dances. In America country dances would be referred to as Contra Dances:
http://www.sbcds.org/contradance/whatis/This is a great source for some music:
http://www.randymillerprints.com/fiddletunebooks.htm NEW ENGLAND FIDDLER'S REPERTOIRE 
168 classic contradance tunes in one source,
with guitar chords. Illustrated with wood engravings by Randy Miller. New 3rd edition, 25th anniversary, 1983-2008.
$22
THE FIDDLER'S THRONE 
A unique collection of 375 traditional tunes from New England, Cape Breton, Scotland, Shetland, and Ireland. Contemporary as well as vintage tunes included. $25
THE FIDDLER'S THRONE--CD 
35 tunes from the Fiddler's Throne book played by Randy Miller on fiddle and solo piano, with guitarists Tom Hodgson and David Loney. $15
Other collections of fiddle tunes include:
Cole's 1000 Fiddle Tunes,
Ryan's Mammoth Collection (the original and more complete version of Cole's), Mel Bay's
Don Messer Anthology of Favorite Fiddle Tunes, Donna Hinds'
The Grumbling Old Woman (Hand to Mouth Music, P.O. Box A, Bedford, MA 01730), Phil Williams'
The Mandolin Player's Pastime, Voyager Publication's
Brand New Oldtime Fiddle Tune Collections, various English country dance collections. Scottish and Irish tune collections also contain useful tunes, as do Canadian fiddle tune books. Many of the collections of tunes suitable for contra dancing can be obtained from Country Dance and Song Society of America, 17 New South St., Northampton, MA 01060; Andy's Front Hall, P.O. Box 307, Wormer Road, Voorheesville, N.Y. 12186; Alcazar, Box 429, Waterbury, VT 05676, and Fiddler's Crossing, if they are not available at your local music store.
Here is a site with some tunes:
http://home.insightbb.com/~otter256/dance/...moon_index.htmlIf you google Contra dance or Contra Dance tunes you'll come up with too much information.