These quality as folk, I believe:

Star of the County Down - I've been properly taken to task for not doing this song correctly and not as well as Van Morrison!
My Grandfather's Clock - I love this old song and sing it every chance I get!
Annie Laurie - one of the prettiest songs of all time.
Buachaill ón Eirne (aka Come by the Hills) and MacPhersons Rant Medley - an instrumental.

I have a few other clips and favorites posted up on Youtube.