With the best intentions in the world as people do their best to preserve these wonderful tunes, errors creep in and are passed on. Often the differences are simply variations because tunes were passed along by ear. It can take a lot of research using many sources to make sure you've got what you set out to find.
largest online collection of info on celtic music, and 100's of links
Henrik Norbeck's ABC Tunes
1661 Irish tunes (in ABC & Midi format)
Irish Traditional Music Tune Index - Alan Ng's Tunography
extensive; well-researched; accurate; Irish session and dance music
The Fiddler's Companion
Andrew Kuntz - songs & tunes in ABC format; plus history, discography, sources, and often several variations
County Champaign Irish Tune Collections Online
Jerome Colburn - closest to session music played hereabouts
Comhaltas Ceoltóirí Éireann
international organization dedicated to preservation of Irish traditional music
JC's Online Music Books
A number of historic tune collections transcribed into ABC notation
The Reverend's ABC Tune Search
ABC Tune Search for Irish traditional music, by Reverend Pete.
Richard Robinson's Tunebook
a collection of traditional tunes, and new tunes in traditional styles - Scots tunes, Irish tunes, Scandinavian, English, French, Balkan and more
Irish Traditional Music Archive
Ireland's national reference archive and resource centre for the traditional song, instrumental music and dance of Ireland
Donagh MacDonagh Song Collection
song lyrics not commonly available elsewhere - collected from radio listeners in Ireland in the 1940's and '50s
Dennis Gormley's "Grab Bag of Tunes"
well-known in Philly, Dennis Gormley is a member of "McDermott's Handy"
Folk Music of England, Scotland, Ireland, Wales & America
Lesley Nelson-Burns' (aka the Contemplator)'s Folk Music Site
McKenna's Irish Music site
bands, musicians, instruments, lyrics, tune books, sheet music, etc. by Hans Jørgen "mckenna" Jensen
Tune Collections in ABC notation
Chris Walshaw - plus learning ABC
Tune Collections on the Internet
Impressive collection of links to other collections
by "Jeremy" - not fact-checked: a lot of mis-information in with the good
Bethlehem, PA - dedicated to the preservation of traditional folk music
Villanova University Library's Audio Collection
Digital archive of Philidelphia Ceili Group's annual festivals and other events available to the public in digital form as part of the Villanova University Library's audio collection. At present (as of February 2016), audio from the 1977, 1978, 1979, 1989, and 1996 annual festivals are available. Recordings from every festival from 1977 to 1996 will be added. Project began in the Fall 2012 and is expected to take seven years to complete.
Now posting recordings of events hosted by the Philadelphia Ceili Group, including: concerts, lectures, poetry, stories, etc.