Mine would probably be The Dubliners’ version of “On Raglan Road” by Patrick Kavanagh. A sad and beautiful song.
Be Thou my Vision
I love “The Minstrel Boy to the War Has Gone,” as sung by John McCormack. Corny, but beautiful.
“Black Velvet Band” by The Irish Rovers. Flip side of “The Unicorn,” which is not on my list of favorites.
Either that, or “Come On Eileen.”
Ditto.
Other favorites?
-“Foggy Dew”, the Chieftans, both versions with Sinead O’Connor and Sarah McLachlan
-“Drowsy Maggie”, Gaelic Storm
-“Toora-Loora-Loora”
-“When Irish Eyes Are Smiling”, Bing Crosby
-“Wearin’ O’ the Green”
Lately, it’s “Big Strong Man.” (informally, “My Brother Sylvest”)
I have a great version from Carbonleaf, always good to get me going.
I’ve been a wild rover for many a year,
And I spent all my money on whiskey and beer.
And now I’m returning with gold in great store,
And I will never play the wild rover no more.
And it’s no, nay, never
No, nay, never, no more.
Oh, I’ve played the wild rover,
No, never, no more.
Wild Rover for drinking. I’m fond of the Dropkick Murphys version.
For sad songs, I like “Brokenhearted I’ll Wander (The Bonny Light Horseman),” the version by Niamh Parsons, which I’m having trouble finding lyrics for.
I can’t just pick one…the links I put in belong to one of our local bands here…good stuff, IMHO.
Drunken Sailor
Jolly Ploughboy
Roddy McCorley
Carrickfergus
Will Ye Go Lassie Go
Johnny I Hardly Knew Ye
I’ll Tell Me Ma
Gallant 40 TWA
Whistling Gypsy Rover
Paddy Works on the Railway (http://www.stoutmen.com/assets/multimedia/Paddy_on_the_Railway2.mp3)
The Mermaid
(http://www.stoutmen.com/assets/multimedia/Mermaid2.mp3)
New South Wales
(http://www.stoutmen.com/assets/multimedia/NewSouthClip1.mp3)
“The Boys Are Back in Town,” Thin Lizzy.
What?
I think it’s Boston Irish, not Irish Irish, but I can’t help think of Great Big Sea’s “The Night Pat Murphy Died.” Grand fun.
I think that one is Newfoundland Irish but it’s a great auld song. 
“Another Irish Drinking Song” by Da Vinci’s Notebook.
“Follow Me Up to Carlow”
And for comedy, “The Orange and the Green”
*One day me Ma’s relations came round to visit me.
Just as my father’s kinfolk were all sitting down to tea.
We tried to smooth things over, but they all began to fight.
And me, being strictly neutral, I bashed everyone in sight. *
Of course, I have tons of other faves, but these are the two I thought of right now.
A few of you folks are posting titles that are Scots in origin, rather than Irish. And some are shanties (probably British.) I point this out just to be pedantic… er accurate, not because I actually care 
I like 'em all.
Raglan Road is one of my favorites. I’m particularly fond of the version done by Susan Hickey, and the adaptation done by Seelie Court (called Sally Gardens.) Also like Eva Cassidy’s version of The Water Is Wide, and the Corrs’ Song For Ireland.
The Sally Gardens is a different air with words written by WB Yeats.
Thank you. I was wondering that, myself. Of course, most of my Scots/Irish songs are from groups that are so ecumenical it’s impossible to guess without knowing the exact history of the song.
(And this doesn’t even get into the point that there’s a lot of cultural contamination between the Scots and Irish…)
“Whisky in the Jar”.
There’s a song I like by Thin Lizzy that I think is called “The Black Rose”. I wish I could remember if that was the exact name.
You’re right, I just looked at the CD and the song I’m referring to is listed as Sally Gardens/Raglan Road. Seelie Court has them combined into one song. It’s gorgeous, regardless.
OtakiLoki the Scots one that stood out for me in particular is Will Ye Go Lassie Go, also known as Wild Mountain Thyme. That song began life as a poem called The Braes O’ Balquhidder, by Robert Tannahill.
“All of the Hard Days are Gone” by the McKrells.
Sorry. I meant your correct username OtakuLoki, of course. Do we have an OtakiLou, or am I conflating people again?