My favorite tunes to play are the airs. My favorites are Foggy Dew and Londenderry Air. What are your favorites?
An Feochan
“As I roved out”
“The Little Red Lark”
“Taimse I mo Chodlaidh”
“Slaibh na mBan”
An Bonnan Bui (The Yellow Bittern)
I just found this one on tinwhistler.com its called The Water Is Wide. The tune kind of reminds me of the titanic theme song 
Joanie Madden’s ‘Waves of Kilkee’ is very nice, too.
There are some good suggestions here:
http://chiffboard.mati.ca/viewtopic.php?t=19781&highlight=slow+air
“Siùl a Ghrà”
“Thugamar Féin an Samhradh Linn”
“Loving Hannah”
“Down by the Sally Gardens”
'Sé Fáth mo Bhuartha ('Tis the Cause of My Sorrow)
Eibhli Gheal Chiúin Ní Chearbhaill (Bright Quiet Eily O’Carroll?)
Carrickfergus (I play it on my A flute or low D whistle–the high notes can get a bit shrill on a high D)
The Factory Girl
The Foggy Dew
Mo Ghile Mear*
MacPherson’s Farewell*
*I’m not sure they’re really airs…
That one’s been throwing me a loop for awhile. Is the air “Down by the Sally Gardens” the reel played slower?
No. Completely different. Google it, it’s a nice little melody. Gets old soon, tho.
Thanks muchly, sir. I can sleep at night now. 
First tune I ever learned on the whistle. It does get old quick but I’m a bit nostalgic for it, I still play it from time to time.
The tune is The Maid on the Mourne Shore.
David
“Brauch na Carrige Baine” and “Roisin Dubh”…airs guaranteed to bring a tear to my eye.
“Siùl a Ghrà”
BTW, what do these words mean?
I also love this tune.
It means “Farewell my love”.
Right now at this early time in my learning it is:
Roisin Dubh
The Foggy Dew
Inisheer
Black is the Color of My True Love’s Hair
This also is the totality of my slow airs! 