I am not a fan of live albums in general. The sound quality is never as good as the on the studio recordings of the same songs, the band often could not reproduce the same sounds as on the record, and too many times the band rushes the tempo compared to the ones on the original recordings.
Sometimes, however, the live recording has something extra. Sometimes the band can really stretch out and show another dimension that the original recording did not have. Sometimes the new live version of the song becomes the better version to the individual listener. Sometimes the band locks into a groove, a mood, a gestalt that raises the live recording to a level above that of the original.
In that spirit, I submit:
The Who---Live at Leeds. Some say this is the best live album ever. The Who get to strut their stuff, showing how constant touring in the wake of the success of "Tommy" formed them into a band of four individuals who thought as one. Really tight musical communication, excellent performances by Pete Townshend, John Entwistle, and Keith Moon on their individual instruments. Roger Daltrey's voice had by this time matured into the instrument that would perform with such great effect on "Who's Next". All rock bands should be this good.
Cream---the live portions of Wheels of Fire and Goodbye. These are the perfect illustrations of the live versions of songs being better than the originals. Cream gets to show why they were called the first "supergroup". Eric Capton shows off his formidable chops, Ginger Baker drums like no one had before, and one of my personal heroes, Jack Bruce, roars out with his unique bass sound and his golden throat. "I'm So Glad', "Politician", "Sitting on Top of the World", and "Spoonful" all illustrate the band at its stretched-out improvising best. "Crossroads" is one of the band's best recordings, and in my opinion is Eric Clapton's finest moment on record, ever.
Peter Frampton---Frampton Comes Alive. I can hear the groans from some of you at this mention. Frampton at this time was being sold as the cute boy of rock and roll with just a bit of an edge so that the older girls would stay interested. Don't let the hype put you off: this is a fine live recording. Frampton and crew were a tight live act, and Frampton himself was a good singer and an accomplished guitarist as well as a writer of good songs. The live versions of these songs are better than the originals.
Mahavishnu Orchestra---Between Nothingness and Eternity. This is my favorite live album. John McLaughlin's bandmates do an admirable job supporting him and their individual solos are not bad, but this is McLaughlin's show. I have never heard him play better on electric guitar, and his tone on this recording is one that I have never heard from him before or since. McLaughlin's playing is stunning, devastating, uplifting, and inspirational. "Trilogy" may be my favorite McLaughlin compostion: I just listened to it again last night and was again blown away. The recorded sound is concentrated in the midrange, and there is some distortion, but no matter. This is a great record. Again, the live versions of the individual pieces are better than the ones done in the studio.