I've compiled a songbook (of course, not by any means complete or indicative of the entire genre) of celtic/traditional songs, most of which seem to go over rather well in pub settings (which is where I learned an unfortunate number of them). This means that of the sixty-some-odd tunes in there, about fifty-some-odd are of the overdone-but-I-know-them-because-crowds-seem-to-enjoy-them type. If anyone would like a copy, I can send it to them. Feel free to PM me about it.

As for specific tunes, I've always been fond of such songs as The Star of the County Down, Ireland (by Garth Brooks, see Roughstock Song Archives for lyrics/chords), and a few other songs, both traditional and not-so-traditional.

-J