Beyounce’s Single Ladies. Absolute perfection.
For me, when I heard Gogol Bordello’s “Ultimate”.
A word of explaination: I had never heard of this band before and I’m not in their target demographic. A friend of my wife (a Ukranian woman with a young kid my wife knows from nursery school) invited us out to see “her friend’s band”. Usually when that happens, it’s a few guys in a bar somewhere doing cover tunes to an audience of their buddies and a few bored drinkers.
It turned out to be these guys.
The first surprise was the venue. The second was the age of the crowd - mostly very young (to us) punky-looking folks. The third was that they were really good, and the first song they did was “Ultimate”. Live, it has a real energy to it. My jaw was on the floor.
The rest of that night was surreal to say the least.
“Blue Sky Mine”: catchy beat, and myself had no idea it was a protest song when I was a younger lass
“Moments In Love”: awesome song with wacky video concept
Many. Last one was Adele - Rolling In The Deep – at a time when almost no one knew her.
Got the link on a Sunday morning and found myself acting like Tom Cruise in “Risky Business.” Though 30 years older and blowing my socks off. 
Thank you for linking that; it was excellent. 11/10 excellent. I have a copy of the CD on the way, and I’m gonna email Mr. Womack and let him know how I found out about him. Can’t say enough good things about how good this good song is :p. It totally fucking rocks!
I was at work when some audio guy played that song. I stopped what I was doing after just 12 seconds of the song had gone by (which is the end of the second line of the first verse) and walked over to ask who it was. Wrote her name and the song name down, stopped by Zia on the way home and picked up a copy. She’s very, very good, but that song is fucking AMAZING; it is transcendent.
I remember walking into a music store in Lisbon, Portugal and hearing this woman belting out a rock song. Holy shit, what a powerful voice! I asked what was playing and they showed me the jewel case. 4 Non-Blondes? Who the hell are they? If it hadn’t been “What’s Up?” playing, I may not have paid any attention to it.
My other revelation in Portugal was the voice of Amalia Rodrigues, the greatest Fado singer of all time and one of the more powerful voices on the planet. Her version of Coimbra. Again, we were fortunate to be able to see her. It was her last concert before her death and her voice wasn’t as good as in earlier years, due mostly to alcohol abuse, I believe. But still amazing.
Alan Parsons Project, the title song from “Freudiana.” Mostly because it was 1991 and I was/am a huge APP fan and I’d had no idea he had made new music. I was listening to this late-night show called “Stone Trek” on KOME and suddenly the unmistakeable sounds of Parsons I hadn’t heard came wafting out of my speakers. I just stared, loving every minute of it and waiting for it to be over so I could find out what it was and where I could get it.
Took me quite some time after that to find the album (at that point it was import-only) but I had to have it.
Also, the live version of Peter Gabriel’s “Signal to Noise.” I’d liked the album version, but when we saw him in concert and he did that one…well, the climax of that song is probably the closest thing to a religious experience I’ve ever gotten from listening to a piece of music.
There are probably a few others, but those are the first two that come to mind.
Neil Hannon’s cover of Life on Mars floored me; ditto Black Box Recorder’s Rock’n’Roll Suicide.
Donny Hathaway “Live”
It is an album(sorry OP) and I am sure most of you have not heard of it but it can be had on Amazon. Donny had a tragic life and his studio albums are not all that great but my OG the first time I heard this I almost crashed the tour van. Not a great recording, there is a round of solos and both guitarists totally blow it but then Willie Weeks makes the bass solo to end all bass solos. Donny plays John Lennon’s “Jealous Guy” and kills it, his “In the Ghetto” is as funky and meaty. I could go on and on, but it is on my desert island five
Capt
Well, you know what, actually? Bohemian Rhapsody.
Lot of good artists there. For me, it would be Europa over Smooth.
Linda solo over her Neville duet.
Alison Krauss could sing the phone book and it would come out beautiful.
The song I’ll put forth is this Fleetwood Mac performance. I wasn’t previously familiar with that song, and certainly wasn’t familiar with how Lindsey performed it live. Like a force of nature.
^^^ Amen to what you said about Alison Krauss! To me, she is the best female singer that there is!!! 
God bless you and her always!!!
Holly (a fan of her since 1994)
Oh here’s one that made my jaw drop but not in a positive way:
Notorious B.I.G.'s “Hypnotize.”
I was watching the “Best Hip Hop Songs of the '90’s” on VH1, and it was the first time I ever heard this song. When I realized the chorus was a sample from my favorite song of all time (Ladidadi by Slick Rick) I instantly wished B.I.G. be consigned to the circle of Hell for thieves.
Alison is also a really fine fiddler, and I’m always amazed at that powerful voice coming out of such a small woman. Oh, yeah, and she’s smokin’ hot!
Forgot to mention it earlier, but the single most profound musical experience of my life was the Bulgarian Voices. I had seen them before at Park West in Chicago, but the second was in the much more intimate confines of a church in Jefferson Park. I got there very early, and was in the front pew. I don’t know how to describe Bulgarian choral music, other then unlike most Western music. These twenty or so women are amazing singers, and the power of their voices from a short distance away moved my wife and myself to tears several times during the show.
Go to Youtube and type in “Bulgarian Voices”. There’s more than a couple videos posted, maybe you can find a good example.
Hey! In case you didn’t know, you can find all kinds of performances that Alison has done at the You Tube website. I love to watch her earlier ones there from when she was still in her early 20s. 
God bless you and Alison always!!!
Holly (a fan of her since 1994)
A couple of the times I saw Prince perform live in the 80s, my jaw dropped. But it wasn’t because of any song.
A sales demonstration CD I had from JVC, meant to show off their better audio equipment in a retail environment, had a song that made my jaw drop. It was by the group Special EFX, a track called Hands of the Healer (also available on their 1987 album Mystique).
What made my jaw drop was the end of the intro, where a clear bell tone seemed to travel thru the room, front to back, while a rumbling bass note shook my bones. A very effective demo of high mid level late 80s audio tech, very well demonstrated by the perfect song for the occasion.
I always like to stumble onto something out of my normal realm of music. Years ago I belonged to a music club and received a Michael Hedges album. Live on the Double Planet.
Among the many songs I liked on it was Because it’s There.
Saw him play 3 times before he passed away (car crash). The last time I saw him was in Columbus and I sat next to a guitar player who actually watched him with his mouth hanging open. He put a great deal of time and effort into his studio work.
The song I like most from my general taste in music is Santana’s Batuka.
Sinéad O’Connor - Nothing Compares 2U will illicit such an emotional response that I really only want to hear it alone. IMO she has the best voice I’ve ever heard and it comes through time and time again in her music.
My usual fair would be Jimi Hendrix’s Voodo Child and Red House
Along the same vein would be Stevie Ray Vaughan’s version of Little Wing which sounds damn good even on my shitty laptop speakers. I’m going to make a point of digging that CD out tomorrow and listening to it in my music room. While I’m at it I’ll cue up Riviera Paradise. This is the kind of music you sit down and listen to with the lights dimmed and no distractions except possibly a glass of wine and a good cigar.