I like Duke Special. He's one man, I know, but he normally performs with a band.
Love Duke Special R4. I missed him joining the Shellac Collective just before Christmas and was really annoyed. He is so unique.
Black 47 was big in the late 90s
Hothouse Flowers and the Waterboys were big in the late 80s
In the late 2000s, there was Flogging Molly...
I hope nobody says The Corrs. Yuck!
Rory Gallagher was fun.
Though not technically an Irish band, but a band that split off from an Irish band: World Party. Karl Wallinger was so beautiful back in the 80s - but like most of us his age, he got quite fat.
Also love the Waterboys. Anyone remember Dexy's Midnight Runners??
Love them, but The Waterboys only had one Irish member. Lead singer/songwriter Mike Scott is from Edinburgh and Karl Wallinger (later of World Party) is Welsh. In addition to U2, I'll add That Petrol Emotion, Hothouse Flowers, Something Happens and The Undertones.
As a teen in Texas in the late '70s, my favorite band on earth was Thin Lizzy. They're still one of my favorite bands of all time. Gotta go with them for the best Irish band of all time.