At the risk of over-generalising I think I have an inbuilt love of a type of music that originates from Ireland.
If I go into detail I fear I might make many factual errors about bands and stuff so I will simply ask this…
Can you reccomend a band/song/cd that has that beautifulm 'irsh’ness about it?
Christy Moore has some good original material, I most strongly recommend, “Live at the Point” if you can track it down.
Loreena McKennitt is actually Canadian, but her music has a strong Celtic influence. If you like Irish folk/new age music, you’ll probably like Loreena.
And another Canadian with strong Celtic influences is Natalie McMaster. But you gotta love the fiddle to dig her.
Seamus Egan - won something like 4 Irish championships in 4 different instruments by the time he was 15!
Solas - a band with the aforementioned Egan
Also, it’s hard not to discuss Irish music without mentioning the Chieftains
Not that I am in any way knowledgeable about Irish music, but I like the above.
A band that’s a bit more Boston Irish, but definately caltic in nature is the Dropkick Murphys. It’s rather punk rock as well, but they have a piper and another bloke who plays mandolin, tin whisle, and dulcimer, a guitarist who switches to accordian when necessary, etc. Theie writing seems to sit in the Irish Drinking and Irish Worker but avoid the Irish Fey stuff. Don’t know if this describes what you’re looking for, but I though it would help. 
U2 of course.
Capercaillie
Altan
The Tannahill Weavers
The Chieftans
Wolfstone
Clannad
Deanta
Cruachan, if you can stomach a little metal.
I was going to say Altan and Clannad and Capercaillie too.
If you love the accent…although a lot of Mary Coughlan’s music is more bluesy than Irishy, she’s from Dublin and no matter what kind of music she sings with that amazing voice, it’s with a wonderful Irish brogue. I love Mary. I’ve met her a few times and she’s a lot of fun. Her voice has this whiskey and cigarettes, “ah fuck it, let’s go have a drink” quality that seeps into your soul. She does a cover of “Mother’s Little Helper” that makes you know that she KNOWS that song.
You might want to see if your local NPR station airs Thistle & Shamrock. Might be some good leads for you.
Love all these bands, except Deanta, who i’ve never heard.
The Tannahill Weavers are, of course, from Scotland. But i’m sure they’re worthy of inclusion in a thread about Irish/Celtic music.
StaberindeMk2 mentioned Christy Moore. I really like the work of Moore’s brother, Luka Bloom. It’s not Irish music in the same way as the more traditional bands above, but it’s interesting stuff and has a very Irish feel to it.
The Corrs.
I highly recommend Maura O’Connell’s music, but for “Irishness” in particular, try her Wandering Home album.
Most of my favorites have been mentioned, but you might also try to find anything by DeDannan; I don’t think they’re still together - I saw them live years ago in Detroit, but they’ve got some good stuff.
Not Irish at all, but in a similar vein, is Stan Rogers. He’s Canadian & does sea shanties/fishing songs/folk stuff. Most of my friends who like Irish/Celtic music also like Stan.
Another good one is Steeleye Span - do interesting covers of traditional songs.
In the same style as the Chieftains are The Clancy Brothers.
Oh good grief. I know musical tastes are subjective but (in Ireland at least) the Corrs are seen as a manufactured pop group. Each to his own though.
May I suggest the Dubliners (before Luke Kelly died). Seven Drunken Nights is a great albulm.
Rory Gallagher’s music isn’t Irish per se but what a performer!
The Golden Horde have a great neo-Ramones sound.
Therapy? offered some strong Irish metal. Stiff Little Fingers for Irish punk (both northern Irish bands).
The Horseslips are well worth a listen as well.
Planxty & Moving Hearts are good as are the early Boomtown Rats. Thin Lizzy were a great, great guitar band.
For the more traditional stuff, I second the Clancy Brothers but really, check out the Dubliners.
I’m surprised to see no mention yet of Tommy Makem, perhaps the single best living Irish folk singer (much the same style as the Chieftains and the Clancey Brothers, with whom he’s collaborated a time or two).
I’m also surprised at no mention of Enya, who’s more New Age-ish. She also happens to have one of the most beautiful voices I’ve ever heard, and I could easily listen to her for days on end, even if I can’t understand what she’s singing (she often sings in Latin, Gaelic, or other languages).