Here are a few of my Celtic faves, be warned I like the gloomy celtic a lot more than the pub songs.
(Irish)
Clannad (Clannad Live, Magical Ring, Macalla)
Altan (Red Crow, Best Of)
Joemy Wilson (Carolan's Cup, Carolan's Cottege, Celtic Dreams -- great acoustic small-group instrumental CDs)
Old Blind Dogs (New Tricks)
(Scottish)
Tannahill Weavers (Capernaum)
Bonus English folk, a bit different from what you think of as Celtic but some of the same roots.
Fairport Convention (Liege and Lief)
June Tabor (Against the Streams)
Richard Thompson (Henry the Human Fly)
Also, pretty much everything on the Green Linnet label is worth a listen (
www.greenlinnet.com)