If you're more of a punk bent:
The Gentlemen
http://www.youtube.com/watch?v=iUi7Fnb2Sz8&feature=relmf
The Dreadnoughts
http://www.youtube.com/watch?v=mBLqV58NudI
The Real McKenzies
http://www.youtube.com/watch?v=1eu0PtSdSNo
The Rumjacks
http://www.youtube.com/watch?v=tDTQQWSmo8s&feature=related
And the all-time classic, The Pogues
http://www.youtube.com/watch?v=L-LuQVKzZMM
There are plenty of others out there, but they're more of an acquired taste.
If you want some folk metal:
Korpiklaani (Don't listen to these guys if you don't have a sense of humor)
http://www.youtube.com/watch?v=OIc4VHxU7iM
Skyclad
http://www.youtube.com/watch?v=OZ2iileann4&feature=related
Ulver (But only their first album. Also, very heavy, and in Norwegian.)
http://www.youtube.com/watch?v=d0_d8KMuOzM
Folk punk, but not necessarily IRISH folk punk:
Mischief Brew
http://www.youtube.com/watch?v=yVnz9bcKeFQ
http://www.youtube.com/watch?v=85srE_w10jA
http://www.youtube.com/watch?v=PpRckbaWfyE&feature=related
Blackbird Raum
http://www.youtube.com/watch?v=462tYMIRtj8&feature=related
Wingnut Dishwasher's Union
http://www.youtube.com/watch?v=FO79S-VPkL0
Andrew Jackson Jihad
http://www.youtube.com/watch?v=EkkjDMXkb60