These may not be on anyone's "favorites" list of ITM (and indeed at least one is probably English in origin), But they are tunes I like well enough to recommend:
Random (Random Notes or Random Jig too all same tune)
Frieze Britches (Freeze Breeches and other variants of the name)
The Big Reel of Ballynacally (sp?)
The Dances at Kinvara (Barn Dance)
The Woods of Old Limerick
Padraig O'Keefe's Slide (The first tune in Sharon Shannon's Blackbird set...not O'Keefe's Slide)
I suppose one should mention Concertina Reel, but frankly I think it is a bit of a bore.
I'm an EC player, so Anglo Players may have quite a different list...
abcs available if needed.