Since this thread has evolved from favourite live rock concerts to favourite live concert recordings, here's my $0.02 (in no particular order):
1. The Who - Live at Leeds
My favourite live rock album of all time! I wore out 2 copies of this album in the 70's. Also had it on 8-track (for the car).
2. Little Feat - Waiting for Columbus
The Tower of Power horns do not disappoint. The quality of the sonics on my copy still blows me away. When I've played this for friends, they are astonished to learn they've been listening to an LP.
3. Deep Purple - Made in Japan
Another classic from my misspent youth. I've lost track of the number of hours I spent skipping school listening to this album! Oh, and discovering girls... ;^)
4. Harry Belafonte - At Carnegie Hall
Recorded April 19 & 20, 1959. This album marked the first time RCA recorded a live concert (comedy concerts excepted) in stereo. They ran the microphone cables from the stage to a recording truck parked in Carnegie's back lot. No live album has ever matched the quality of this recording (you might not like the music, but that's another matter entirely).
5. Sarah Vaughn - After Hours at the London House
Recorded March 7, 1958 in a live after hours session at the Chicago club. There was a screw up and the sheet music didn't arrive, so the band simply jammed the entire set! You wouldn't know it however by just listening to them. Half of the musicians were from Count Basie's band.The session started around 2:00 AM and went to 5:00 AM! At one point, Sarah forgets the words to a song and they have to restart twice.