You can't write about songs of Northern Ireland and not include Danny Boy. The song (or at least the tune, the Londonderry Air, now almost synonomous with Danny Boy) is used as Northern Ireland's anthem in the Commonwealth Games and one or two other sporting events. I think I also remember reading the Londonderry Air was also used by the Northern Ireland government (when it was in existence), but this could be wrong and I can't find reference to it now.

Danny Boy is apparently one of 100+ songs composed to the same tune, the Londonderry Air. It was written by Frederic Edward Weatherly, an English lawyer, originally in 1910 to a tune of his own writing. It wasn't very successful. In 1912 he received, from his sister-in-law who was in America, a copy of the tune The Londonderry Air which fitted his song nearly perfectly. He made one or two small changes and republished Danny Boy to the tune of the Londonderry Air in 1913. More on the history of Danny Boy / the Londonderry Air can be read cortesy of Limavady Town Partnership.

Weatherly isn't ever recorded as actually having visited Ireland, but nevertheless Danny Boy has gone on to be sung throughout the world by ex-pats of Eire and Ulster; in fact this was Weatherly's intention as he had expressed a hope that "Sinn Feiners and Ulstermen alike would sing his song". In fact it's so cross community I'll go so far as to say that the best version I've heard is by the Pogues, as it's got a slightly faster rhythm than any other versions I've heard and just generally sounds more lively.

Follow up:

Danny Boy
Frederic E Weatherly (listen here)

Oh Danny boy, the pipes, the pipes are calling
From glen to glen, and down the mountain side
The summer's gone, and all the flowers are dying
'tis you, 'tis you must go and I must bide.

But come you back when summer's in the meadow
Or when the valley's hushed and white with snow
'tis I'll be there in sunshine or in shadow
Oh Danny boy, oh Danny boy, I love you so.

And if you come, when all the flowers are dying
And I am dead, as dead I well may be
You'll come and find the place where I am lying
And kneel and say an "Ave" there for me.

And I shall hear, tho' soft you tread above me
And all my dreams will warm and sweeter be
If you'll not fail to tell me that you love me
I simply sleep in peace until you come to me.

I don't want any comments suggesting the Northern Ireland football team should adopt this as a national anthem either, the debate of God Save the Queen vs Danny Boy has been done to death over at the Our Wee Country forums.