Might be just bad memories, but I have to say "Cry Love" by John Hiatt. And of course, "Oh Danny Boy" needs no mentioning. You'd have to blackhearted or British not to feel a bit broken after hearing it. Oddly enough, the song isn't even of Irish origin really :/
I downloaded a couple songs I'd never heard of from this thread, because its one in the morning, and I'm exhausted, and I don't want to go to bed. Sleep is my newest enemy
Before I comment, I just want to admit I have no taste. I hated Ruby's Arms. I could only stand a little over three minutes of it, before silencing it with a wince. It was like a a spoonful of mayonaise for my ears. Flogging Molly was alright, but I was expecting something with more of an Irish sound to it for some reason, like The Blood Of Cu Chulainn or something. I did like Morphine "In Spite Of Me" though.