Not an amateur, but once when I saw the show (in Chicago, but I can’t remember what year, and therefore can’t remember what actor, darnnit!) the actor’s mike went out about two lines into the song. There was an audible gasp from the audience as the sound system made a few crackles and then went totally dead. The actor, bless his classically trained heart, paused less than half a rest as he realized what was going on, and then he readjusted his technique…and we could hear every note. Every note, all the way back in the student’s cheapie nosebleed seats. It. Was. Amazing. The only thing more amazing than that song is that song unplugged. Just chilling.
Nessun Dorma is a good one. Thinking of that reminded me of the Three Tenors which made me think of O Souverain which would be one I’d love to be able to do perfectly.
Because they would be listening. They’d be avoiding making any noise whatsoever. To continue the metaphor, just like a girl who is totally into you. If she’s actually bored, she’s going to be trying to do something that boredom, even if it’s just fidgeting.
Good question – I do this all the time every week. Especially for 1970s soulsters like Billy Preston and Dr. John – the kinds of keys they tend to play behind their tracks aren’t really designed to be played w/o vocals or horn hits and riffs. Most people seem to enjoy hearing stuff they recognize, though, even though it can be a bit of arranging-on-the-fly to cover the standard arrangements using RH on whatever board you’re playing.
Hey Jude.
“Run” by tin machine. After which I’d get a bunch of blank looks, I know.
American Pie

Free Bird!! So I could shut up the drunk asshole at the bar.
ETA: Okay so I re-read the OP and apparently we’re not at a bar. Still, Free Bird would be a sick song to play flawlessly.
This would make my night, not that IASTHANKFUL I don’t get the “Freebird” when playing small combo covers.
Billy Powell ruled it on this one, but also, “Give Me Three Steps Back” – or something, something, something. Got to rememember that one to get some payback from the stage:D
What else would you do? This almost sounds like if you were Zach Galifianakis and suddenly grew a pair and some bigger balls to defy the audience. I wish I didn’t need those assholes as much as I do now. Let me know?!!
I would love to be able to play the guitar like Django Reinhart .
For singing, pretty much any song Aretha Franklin belts out I would love to do. It would look hysterical coming from a blue eyed, reddish haired white woman, though.

Whammer Jammer or Juke. I play harmonica a bit and those are classics.
I play AT harmonica - I wouldn’t say I play it. I dig Whammer Jammer, but this one is amazing, and I would definitely pick this to ‘nail’.
Lost Fox Train
Wade Schuman is incredible.
Walk A Mile In My Shoes.
performed by many, written by the great Joe South.
"Rollin’ and Tumblin’ " just like the late, great RL Burnside – or even Kenny Brown.
With Bob Dylan’s lyrics, circa 2006.
The lights go down. It’s just a single spot on me. And then a small pin-ray spot picks out SWMBO in the audience. And I sing to her.
As I posted on that clip:
When I was first courting my sweetie, I brought my guitar over one night and played for her. This was the last song I played that night and she tells people to this day that it was during this song that she fell in love with me.

And while it might seem a little sappy to some, getting up in front of 100,000 enthusiastic people and belting out a perfect “Star Spangled Banner” would be something I’d remember for a long, long time. No instruments and no clowning around (“brave” does not have 73 syllables, thank you very much).
You know, I saw this thread when it was current but I never could come up with an answer. There’s a whole lot of songs I’d like to sing. The other day, I got to wondering what everyone else had said, and so here we are again.
If we only get one choice, I really like Valgard’s answer. When I read it, picturing the audience who would be so into it, I suddenly flashed on that scene from Stephen King’s The Stand where the Boulder Free Zone has assembled for the first time…wow.