My contribution: anything from the album 11-17-70 by Elton John.
Also, I’ve heard that Karajan conducted a highly regarded version of “Thus Spoke Zarathustra.” Probably a studio recording, so may not fit OP, although I think the performance is essentially live (no overdubbing, etc.)
“Army” from Ben Folds. I like it when artists get the audience involved.
“Piano Man,” by Billy Joel. I’ve seen him live twice, and it’s amazing to hear the crowd start singing the chorus, spontaneously.
“Man of Constant Sorrow” by Alison Krauss and Union Station. I was at the recording of this live CD/DVD, and it was phenomenal to hear. Especially since it was recorded in Louisville, KY, and Kentucky gets mentioned in the song.
Give up the Funk (Tear the Roof Off the Sucker) - P-Funk All-Stars, from Live at the Beverly Theater. Played a bit faster than the album version, with full horn section, and an epic jam at the end. This is the only George Clinton live album I’ve ever heard that truly captures this band doing what they do live, and not the sanitized exactly-as-on-the-album-but-with-crowd-noise like all other Parliament/Funkadelic live albums that exist.
“Cheap Trick at Budokan” is a terrific album. Their studio albums were meh, except for the debut which was quite good. The one live show of theirs that I’ve seen was also disappointing.
Yeah, if you can’t play it live, how good a band are you, really?
facist
Ok that’s out of my system, my first recommendation technically is an album, but I’ll make two specific recommendations. Every song off it is my favorite recording of that song by any artist.
It’s We’ve Got a Live One Here by Commander Cody and His Lost Planet Airmen. It was put out on a major label, but it’s still obscure enough that it doesn’t have a Wikipedia entry. It does appear to be available for purchase on several digital platforms. The band were all great musicians, and they knew the three concerts these recordings were picked from would probably be their last hurrah. All of them are absolutely there in these recordings.
If I was able to link to my favorite live recording from it, it’d be “San Antonio Rose”, because it’s beautiful. You can hear the band change styles from Western Swing to Ranchera to New Orleans Jazz and back again through the solos. But, my favorite single song isn’t on YouTube. I did track down the version of Smoke! Smoke! Smoke! (That Cigarette) that Warner hasn’t smooshed yet. So, go listen now. My brother commented that it’s amazing they could play the song that fast and still so damn tight. He’s right, they work that song hard.
Erroll Garner - Night and Day from the remastered Complete Concert By The Sea. This song opens Disc 1 instead of I’ll Remember Apri which was the first track on the original 1956 release.
Univers Zero - Xenantaya from 2006’s Live. There were no videos I could find for this song so I made one. Fair warning: this is a 13 minute song. Obviously IMO it’s worth the time.
Too Many Zooz - Brasshouse (at least I’m pretty sure the this is considered one of the versions of Brasshouse). This is the recording that went viral and I still love the performance. Matt Doe, the trumpet player, isn’t even with them in this recording; it was a busk session that a passerby recorded and posted.
David Bowie, “Width of a Circle”, off Santa Monica '72. About 8 minutes of Mick Ronson really cutting loose, with Woody Woodmansey and Trevor Bolder his able lieutenants. Oh, and some bloke called Jones sings.
Aw, fuck yeah. Gotta include the track right before it, Lights Out.
For me, I’ll go with The Rolling Stones, the Brussels Affair live recording of Tumbling Dice: - YouTube
A definitive live example of Mick Taylor/Keith Richards guitar weaving, and NOT weaving - where Taylor plays gloriously fluid leads on top of rock-solid Keith rhythm work. So wonderful.
As for jazz, well, probably the most famous jazz solo is the Live Newport Jazz festival recording of the Duke Ellington Orchestra, playing Diminuendo and Crescendo in Blue, featuring 27 choruses by brilliant tenor sax player Paul Gonsalves. Here’s a link to a Youtube vid that not only has the song, but has the story of the event running as the song plays and it is excellently researched: A Famous Solo by Paul Gonsalves - YouTube. The underlying narrative about Ellington’s career and what this event did for him, and his interplay with the stage manager is just amazing.
Cheap Trick is an awesome live band, though their live performances can vary a great deal. I’d have to go with “Ain’t That A Shame” from Silver. Most of the performance was sweetened, but I’ve seen them do it equally as well live.
Another choice would be Elvis Costello’s early live version of “Accidents Will Happen.” It’s not perfect, but it’s a heck of a recording and a great alternate version of the much-faster album version.
This was the vision that Bill & Ted had where music would bring together all cultures in peace and harmony…BabyMetal and Rob Halford duet of ‘Breaking the Law’