Just a few for starters:

Hornpipes
Set: Jimmy Allen & Newcastle
Off To California
Reels
Billy in the Lowground
Devil's Dream
Drowsy Maggie
Mason's Apron
Jigs
Banish Misfortune
Swallowtail Jig
Morrison's Jig
Marches
Bonaparte Crossing the Rhine (or Alps) (March)
Slipjigs
Another Jig Will Do
The Butterfly
Waltzes
Amelia's Waltz
Midnight on the Water
Southwind (really an air, but many play it at the faster speed of a waltz)