Banjo tune defined: a song with a banjo on it, for oh, at least half the song, or more. I always find it hard to chose an absolute favorite, of anything, but right now this is mine: “Green Mountain Hop”, by the inimitable Don Reno.
It’s joyful. It’s sad. It’s angry. It’s alive, and it’s amazing.
Bela Fleck and the Flecktones
Sunset Road
Half Moon Bay
Reflections of Lucy
Their band has the distinction of having one of the best banjo and harmonica players and for sure the number one best bass player in the world Victor Wooten though he shows off more in his solo pursuits than in these songs.
I submit Rag Pickings, performed by Fred Van Eps.
~Max
Journey Of The Sorcerer.
My favorite banjo tune is by a one-man project called No One Gets Out Alive; he plays Banjo Slam. Here’s My Rifle, My Banjo and Me!
That’s a good one.
~Max
It’s a toss up between Foggy Mountain Breakdown and Sweet City Woman.
Darling Cora:
Banjo tune, huh? Geez, I have so many favorites it’s hard to pick. 
When I was about a Junior in high school I bought a 45rpm record of Steve Martins “King Tut”. The B-side had 2 songs Sally Goodin’ and Hoedown at Alice’s. Always thought they were decent.
Anything by Stuart Griffin is mighty fine as well.
Pete Seeger’s “Banjo Medley”. It’s almost meditative like a sitar raga.
To listen to or to play? 
My favorite to play varies from day to day. Lately I’ve been working on Tui’s version of Smoke Behind the Clouds.
Can’t begin to list a favorite bluegrass/oldtime tune. I’ll offer up anything by The Carolina Chocolate Drops, Lucas Poole, Tui, and countless others.
So instead of trying to pick on of those, I’ll go in a completely different direction and pick Blow You Away by the Supersuckers. A fun driving tune by the self-proclaimed “greatest rock and roll band”!
A few thoughts so far.
On Bela Fleck: I first read about him in 1979 or so, when he appeared out of nowhere on the cover of Banjo Newsletter. He’d only been playing a few years, and was already the best in the bluegrass business. I lost track when he went on his unique path, but have occasionally heard his stuff. Great choices there. Not exactly my type of banjo music, but I do appreciate it.
Fred van Eps: This is where banjo jokes started. Oh, I think it’s cool, but I can see how others might find it annoying as hell. 
I do like some of his later playing better, like some of his stuff from the 50s.
Steve Martin: Without going into details, there are two popular ways of playing the banjo, three-finger picking, and clawhammer (sort of a pluck and strum combination). Martin plays them equally well, and is as good as any banjo player I know. Professional level playing. Love him.
Pete Seeger: Second only to Earl Scruggs of Foggy Mountain Breakdown fame in re-popularizing the banjo after the immenssley popular banjo orchestras of the early 1900s. He is playing in the clawhammer, or frailing, style I mentioned. Good stuff.
Smoke Behind the Clouds: More clawhammer. I love this style, but have no where near explored it enough. Thanks for posting, this sounds like a good place to re-ignite my interest. Reminds me of the awesome John Hartford/Bob Carlin album, The Fun of Open Discussion.
The Ballad of Jed Clampett. 'Nuff said.
Dawggy Mountain Breakdown, a.k.a. the theme to “Car Talk”.
(Damn I miss “Car Talk”… 
)
Get A Load of This – R. Crumb and his Cheap Suit Serenaders
Wow, can he cut loose!
Loved Car Talk, never loved the theme. Now I realize it might be because we only got to hear a bit of it, and it ruined the full effect of the tune. This sounds so much better!
Be courteous kind, and forgiving,
Be gentle and peaceful each day…
Get all excited and go to a yawning festival.
Be oblong and have your knees removed. Everybody! Let 'em hear you outside.
See, though, Steve even strums the banjo on a professional level.