The Lark in the Morning (jig)
Morrison's Nos 1 and 2 (jigs)
Am Phis Fhliuch (slip jig)
Mountain Road (jig)
Jenny's Picking Cockles (reel)
Austin Tearney's (reel)
The Earl's Chair (reel)
Maire Breatnach's (reel)

I know that's only 8 but I can't think of any more 'old favourites' just now. Most of them can be found in 'O'Neill's' book