Being an air-head as I am (that is, a tin whistler not good enough to play reels), how about your favourite 1000 tunes (give or take)…
TB
SDG
I remember back when I was an “air-head” myself now I can play reels but still get joy from the old airs. Here are my favorites in no particular order:
For ireland I would not Speak Her Name (probably my all time favorite)
Give me your Hand
Cariickfergus (hard on whistle but I now have the skill to play it)
The New Dresser (a new tune I found in Merlin Music’s session Book 2
http://www.merlin-music.com)
Westomoreland
The Dark Isle
Sir John Fenwick
The twisting of the Maypole (english title can’t spell the Gaelic one)
The Heart is True (very very hard to play but a very nice tune worth the effort)
The South Wind
Now for all the O’Carolans:
Si Bheag Si Mhor
Hewlett
Planxty Irwin
O’Caolans Draught
The Wounded Hussar (in G minor [two flats] the only version I have it is very hard)
Blind Mary
O’Carolan’s Concerto
That is all I can remember right now there might be more. 
Favorite airs? My lord, where do I start . . .
Buachaill on Eirne
An Ghaoth Aneas
Baidin Fheidhlimidh
Fainne Geal an Lae
Eanach Chuin
Gile Mear
Carrickfergus
Coinleach Ghlas an Fhomair
Sally Gardens
The Snowy Breasted Pearl
There are dozens of others I like that I can’t think of right now. Some, to me, sound better on the whistle than, say, the fiddle – but that’s just my opinion.
Will O’Ban
Inisheer is a pretty one.
One I love to play and sounds much “wilder” to my ear than Inisheer is Ar thaobh na Carraige (By the side of the rock) from the Dossan of Heather tunebook.
Susan
Banks of Sullane (as played by Jackie Daly).
Steve
My current favorites are Poor Irish Boy, An Raibh Tu ag an gCarraig, Fair Maid of Wicklow, Ardaigh Cuain and Month of January.
We have similar taste it seems Will 
Many of yours are my favorites too. As of late, I’ve been working on “The Parting Glass” which I think is also very pretty.
“The Parting Glass” is nice. I also like Kate Hepburn. 
Will O’Ban
P.S.: Since changing your avatar, Izzy, it makes my liking Kate Hepburn comment (concerning our similar tastes) seem out of place.
The Dawning of the Day and Cliffs of Doneen.
When Larry Nugent plays them, I like Spailpin’s Lament and Banks of the Suir and Cape Clear.
Two more of my favorites.
"Fainne Geal an Lae " I believe is roughly translated as “The Dawning of the Day.” Yet, I think they are two separate tunes. Does anyone know if this is correct? 
Will O’Ban
It’s funny that you mention it. It wasn’t but a couple week ago where I was reading the notes of “The Dawning of the Day” in some book and thought, 'Hey, I know that tune". Of course, I knew it as Fainne Geal an Lae, but as I was writing my post I couldn’t remember how to spell that. So, for the sake of this post, the one that I like is Fainne Geal an Lae… if they’re the same tune, then I like “The Dawning of the Day” too.
Oh, and I didn’t see it in your initial list or I wouldn’t have put it in mine 
That’s quite alright . . . we’re all entitled to like the same tunes.
I just thought I’ve seen music for “Fainne Geal an Lae” and “The Dawning of the Day” and they seemed like different tunes in spite of having roughly the same name. Or maybe I’m mistaken?
Will O’Ban
Phew, I’m glad
I might as well be the first to add The Skye Boat Song. I know, I know. It’s like saying Danny Boy, but I can’t help but like it.
I like the Arran Boat Song.
“Fainne Gael an Lae” is the “Dawning of the Day”. There is a song called “Raglan Road” that also uses the same tune.
Favourite airs:
Árdaí Chuain
My Lagan Love
Ar Éirinn Ní Neosainn Cé Hí
djm
Fainne Geal an Lae (literally “The Bright Ring of Day”) is the one usually translated as “The Dawning of the Day.” Is it possible the other one you’re thinking of is “Níl Sé an Lá” (“It is Not Yet Day”)?
Redwolf
I know that I’ve seen this version of “Dawning of the Day” someplace
else, but in my current search I found both tunes in Walton’s 110
Ireland’s Best Slow Airs. Dawning is on page 40, and Fainne is on page
55. Are these not different tunes, or Is my mind playing tricks on me again?
Will O’Ban
They have slightly different rythms and are in different keys (one is major one is minor) other wise they are the same.
That’s just lovely . . . I pay for 110 slow airs but only get 109.
Will O’Ban