Care to share your all time favorite (at this time) Trad tune ? Mine’s (att) Song of the books’ (Valentia Harbour) as played by Boys of the Lough http://grooveshark.com/#!/s/Valentia+Harbour+The+Jug+Of+Punch+MacArthur+Road/3pCDGk?src=5
January Snows by Lunasa
guaranteed to melt any snow if the volume is turned up
Well, there are a few oldies but goodies and then there is… Brian Finnegan & the Best of Bath - Back to Belfast
http://www.youtube.com/watch?v=kmFf_vpsr9I
Sweeeeettttt! 
You’re not fooling us. You just like the Muppet Show theme at the beginning. 
who doesn’t like the Muppets?.. speak your peace or forever hold your tongue.
Whatta an intro…!
Tar Road to Sligo.
I usually play it several times a day.
(I almost sound good too.)
Drowsy Maggie. This one definitely shakes out the cobwebs.
So hard to choose just one, but among the very top for me:
Drúcht Na Maidne (The Morning Dew, aka The Hare in the Heather), especially as played by Éamon De Buitléar & Ceoltóirí Laighean
The Frieze Breeches (aka Cunla), especially as played by Séamus Ennis or Liam O’Flynn
The Blackbird (many different versions of this but Paddy Keenan’s is my favorite so far).
Interesting some pick a tune and some pick a recording. Two different things, those.
Cooley’s Reel by far. Really cool modern recording of it can be found by a Celtic metal band called Eluveitie if anyone has heard of them. They play it in B Dorian instead of E, encouraged me to go out and get an A whistle
Right now my favorites are the ones I’ve found to have an interesting history or influence on other music. For example: the melody for “Star of the County Down” is used for the song “I Heard the Voice of Jesus Say”. And “Slane” is the melody for “Be Thou My Vision”. “Lord of the Dance/Simple Gifts” has an interesting history too. (The OP didn’t say it had to be Irish Trad.)
Agreed - I especially like ‘Otter’s Holt’ because it’s the melody of ‘Take her in your Arms’. Also because I recently reread ‘Tarka The Otter’ (originally read when I was a teenager) and discovered what an otter’s holt is (its home), and that otters used to be hunted with dogs 
When first I saw this topic I thought you were asking which tune I preferred to play. I struggle with finding a single favorite for listening as that list would be long. Since Gumby addressed my point and others have offered alternate views I’ll go along with the following:
My favorite tune to play is The Foggy Dew as it can be easily played in so many different tempos and used as a dramatic emotionally evocative march, a fun dance, or a slow dreamy waltz-like piece as necessary. My favorite version of it is by the Chieftains/Sinead O’Connor. A close second would be Roisin Dubh.
If I had to pick one favorite for listening, it would have to be the live “sound sample” on Michael Burke’s website by Flutio McCoy/Kells - Amhrán na Leabhar/Fermoy Lasses. Not very trad but amazing nonetheless.
ecohawk
“Caberfeidh”
Now that you mention it, that is a great tune to play and listen to! It’s easy to forget about some of these when learning new ones.
Another worth mentioning IMO is The Eagle’s Whistle. It makes for a nice march and slow tune, whatever the mood calls for. 
Black Pat’s Reel, The Golden Castle, Jimmy’s Return, The Bucks of Oranmore, Julia Delaney’s, Laura Lynn Cunningham, The Humours of Tullycrine, Maids of Mt. Kisco, and probably about 30 others could go on my list of all time favourites.. hm, but I just woke up.
All time favorite Trad tune ?
Really?? Okay… The College Groves - especially when played rather slowly and with a “lilting” feel, for example as by Mr. Russell.
I’m hard-pressed to pick and all-time favorite, but my favorite tune of the moment is John Brady’s jig.
Yes as Mr Gumby said, it can be two entirely different questions, which is one’s favourite tune from a trad band’s album, and which is one’s favourite tune to play.
And perhaps the second could be divided into two 1) your favourite tune to play for others, your “party piece” 2) your favourite tune to practice or play when alone.
Concerning the first one, usually with reels and jigs it’s hard to parse out an individual tune from a set, at least for me. So it might have to be one of the “big” jigs from one of those old Chieftans albums, Cherish the Ladies or The Gold Ring. Or a “big” reel like Trim the Velvet from Gay McKeon’s album.
As for playing for others, when I’m out playing somewhere and somebody asks me to “play a tune” it’ll likely be The Morning Dew.
When I’m by myself and I pick up the whistle and just tootle, it’ll likely be Buchimish (in 15/8) or nowadays Sandansko Horo (in 22/8). I just like those “crooked” tunes.