Caveat: Listening is practice too! If all you do is regurgitate stripped down versions of tunes your playing is going to be rather bland. So, combine this play along practice with lots of listening to the masters of the style to drink in subtleties that don't come through in tutorials. What this play along practice will do is allow you to participate more in sessions. If you can participate more, you'll have more fun and want to attend more. When you attend more you learn more. It's exponential!
Irish Play Along Tracks
Comhaltas Foinn Seisiún: Traditional Irish Session Tunes by Le Ceoltóiri Cultúrlainne
Volumes 1, 2 and 3 contain over 325 traditional Irish session tunes arranged in sets and played by musicians from Dublin and Ennis. The tracks are pretty fast and straightforward - just below full session pace. Features several melody instruments playing at once for an authentic trad sound. Most of the tunes played at your local Irish session are bound to be among the 325 covered here. Rhapsody: Volume 1, Volume 2, Volume 3.
Tenor Banjo - Sets and Tunes Part A and B by Johannes De Wal
This stripped down recording of tenor banjo, bodhran and a few other instruments is a good source to hear many of the more common session tunes as played on tenor banjo. 66 tracks containing over 135 tunes played at a medium pace complete with obligatory triplets and other ornamentation. Streams on Rhapsody: Part A, Part B.
Slowplay Jigs Reels and Hornpipes by Jeffrey Hillgrove
Relaxed, moderate tempo. Guitar with bodhran accompaniment. Good selection of popular session tunes. Rhapsody link.
Slow and Easy by John Weed, Stuart Mason
Slowplay fiddle with rhythmic backup guitar in DADGAD tuning. Streams on Bandcamp!
SlowPlayers Session Tunes volume 1 - William Bajzek - flute, Angeline LeLeux - fiddle
Reels, jigs, hornpipes and polkas played slowly. Also streams on Bandcamp!
Tunes for Practice - Seamus Creagh
69 total tracks played slowly but not too slowly. Each tune is performed plainly and then with ornamentation. Great tutorial. More info here.
Old Timey Fiddle Tunes Site
Fairly comprehensive collection of field recordings, direct from expert sources and workshops. http://www.mne.psu.edu/lamancusa/tunes.htm
Nashville Oldtime Music Association
This group has gathered numerous old-time tunes in its mp3 "jukebox" for streaming. Recording quality is sometimes sub-par, but the arrangements are spot on. Here's the link.
Public domain mp3 files from this long running jam in Pegram, TN. You may need a password to listen. If you have trouble logging in contact me directly; I might still have the log-in info that allowed me to access the tracks. http://pegramjam.com/tunes_by_name.html
Charlotte Folk Society
They have posted audio samples of the tunes from their monthly slow jam. http://www.folksociety.org/slowjam.shtml
The Flatpick Apprentice Blog
This blogger and guitar flatpicker has put up some fiddle tune rhythm practice tracks at varying tempos. Sorta bluegrassy. http://flatpickapprentice.blogspot.com
Mandolin Instruction: Old Time, Country and Fiddle Tunes by Michael Holmes
Audio files from a classic 1970's tunebook. Features a lot of the core tunes. Streams on Rhapsody here.
Wendy's Old-Time Tunes List
Site containing a long list of old-time tunes and links to where you can hear them. By clicking on Wendy's links you'll find out about even more play along sites that aren't covered here. Link to Wendy's links.
Contra Dance Play Along Tracks
Portland Play Along Selection
97 tunes selected from the two excellent Portland Collection tunebooks. These are my all-time favorite play along recordings! A wide variety from standards to obscure, from traditional to recently composed, from Celtic to Appalachian to Maritime and more. Played at about 20% below session speed but still very musical. Features Clyde Curley on mandolin and tenor banjo. Purchase here.
Over 100 tunes representing the essential repertoire of New England dance music. Nonetheless, this project likely includes some classic cuts from your local session or fiddle tune jam. Details here.
If I've omitted any really good sources for ear playing let me know and I'll add them!