Well there are so many to choose from:
-U2
-Snow Patrol
-The Script
-Bell XI
-The Blizzards
-The Coronas
-The Saw Doctors
-Republic of Loose
-Fight Like Apes
-Thin Lizzy
-The Pogues
-Ash
-Director
-The Horslips
-Boomtown Rats
-Industry
I think that my favorite is Celtic Thunder. There is also a group called high kings ( another grate group)but they are much more traditional irish music its all up to you on what one you would like.
Celtic Thunder, Celtic Woman, The Pogues, U2, The Cranberries, Flogging Molly, Dropkick Murphys, Clannad, The Chieftains, and Gaelic Storm are good Irish bands.