How to begin, I can only list some of my favourites which is probably a tip of the iceberg. You might want to go to the Ceolas website (see link section in Mudcat) or try the Irish trad links there. You may also want to see rec.music.celtic for what people are talking about.
Anyway, some I like
Dervish Nomos - Niall Vallely is possibly one of the best concertina players I've seen - his solo CD is very good.
The obvious also: Planxty Bothy Band Andy Irvine Kevin Burke / Patrick Street Christy Moore
and now my mind goes blank. Anyway enjoy searching around