There are a few one-shot tunes you need to work up -- tunes that you'll want in your arsenal for emergencies, even if you don't plan to play them.
At weddings and other parties, at dances and while you're busking, folks will come up and make requests. It's their money, you should try to earn it.
The single-most requested tune? Happy Birthday. Learn it in G. It's easy for everyone to sing there, and it lays out nicely.
Foggy Mountain Breakdown and Dueling Banjos are common requests from drunks. On the street, it's usually right before, "Shay -- can, can I play yer guitar?" even when I'm playing mandolin.
From sober, or at least soberer, people, I get requests for Irish tunes or for the Beatles.
For tunes I don't want to play, or that are out-of-genre, I say, "Ask the fiddler. We only play tunes the fiddler knows." I blame someone else. They're understanding and end up feeling like we'd honor their request if we could. Unfortunately, one of us just doesn't happen to know that particular tune. Dang.
And if the fiddler does know it, we just play it. What the heck. If it's the Beatles, and the requester is female, she'll often want to sing. If it's a wedding or other party, where the guests know one another, we usually say "Sure," and hand her a mike. Not uncommonly, folks will sing along, or it'll be the sister of the bride, and you end up with a huge tip. You earned it. You made folks happy.
Learn a waltz that everyone will recognize. Jay Ungar's Lover's Waltz is "Oh, that was from that Civil War series that was on TV, right?" The Tennessee Waltz is a win. We're from the Southwest, so we can get away with doing Cielito Lindo. Don't play it too slowly, either. Until you learn how to play waltzes the right speed, ask some dancer in the crowd that you know to signal you for a speed adjustment.
Learn a hambo. Dancers will come up to you at the breaks and ask for one. The biggest complaint I've heard from Scandy dancers is that old-timey bands play Hambos like waltzes -- too fast and with the accent on the one, instead of the one and three. Think "ONE two THREE-ONE two THREE-ONE two ...." And think it slowly.
Occasionally, you'll get a request for a schottische. There are fine schottisches, so add one to your repertoire. When you can't think of how it starts, a hornpipe like Off to California will work if you play it slowly, and dot it heavily. Go dance one first, and it'll become obvious what you need: step-step-step, hop / step-step-step, hop / step, hop, step, hop / step, hop, step, hop .
Learn a swing tune or a rock-and-roll tune or something else danceable to throw in at a occasion break.
Dancers will thank you and come away thinking you're versatile. Plus, many of these are slower, singing tunes, which are crowd-pleasers that don't go well with "All join hands and circle to the left!"
Spending a few minutes listing these out and agreeing on them makes every spur-of-the-moment, "Okay, right after this, 'Happy Birthday, in G' " smoother and less stressful. It transforms the hurried, dead-air, "Can anybody start ...?" into a nod of the head and a "Ready, boys?"
I have a fond memory of a playing a gig with Fergus Stone -- perhaps the only banjo player I've ever met who can play credible clawhammer, old-timey two- and three-finger, and Scruggs-style bluegrass -- at which some drunk had come up and requested Foggy Mountain Breakdown. Before I could get out, "Ask the fiddler," Fergus was half way through the tune.
