A little more. Much of the information below comes from Andrew Kuntz' The Fiddler's Companion, which is the best place to start looking for background on dance tunes.

Earlier discussion here in the Forum, including Gaelic text of Máire Ni Eidhin as referred to above.

Cluck Old Hen: Text in the Digital Tradition database: CLUCK OLD HEN
At The Fiddler's Companion: Cluck Old Hen (search results)

Old Molly Hare is an American variant of a tune first published c.1805 by (and attributed to) Nathaniel Gow, as The Fairy Dance.
In the DT: OLD MOLLY HARE (OLD MOTHER HARE)
At The Fiddler's Companion: Old Molly Hare (search results)

Shady Grove is known in a number of variants, some of which have associated lyrics. Type shady grove into the "Digitrad and Forum Search" box on the main Forum page, hit GO and start reading...
At The Fiddler's Companion: Shady Grove (search results)

Over the Waterfall was apparantly used for two stage-songs; The Feller That Looks Like Me (USA) and The Dark Girl Dressed in Blue, which is probably the original title (UK; by the Music Hall performer Harry Clifton, 1824-1872, who is also credited with a number of other songs which have found their way into tradition).
At The Fiddler's Companion: Over the Waterfall (search results)

June Apple: presumably the Old-Time breakdown? There is a snatch of verse sometimes sung to the "b" part:

Wish I was a June Apple,
Hanging on a tree,
And every time my true love passed,
She'd take a little bite of me.

See also these previous discussions for more:

June Apple lyrics?
Lyr Req: June Apple

Black Mare of Fanad. A Donegal name for the reel more usually known as The Nine Points of Roguery. Never used for any song that I've heard of.

Free Little Bird As recorded by Dykes Magic City Trio; at Roots of American Fiddle Music.

After a bit of practice and perseverance with search-engines (the one here that I mentioned earlier is very useful, though not indexed as often as we might like) you will be able to find this sort of information for yourself. Although many dance tunes have at one time or another had songs or snatches of verse associated with them, a great many never have.