This thread has been around so long, I can't remember if I already went!
In case I didn't, or in case my view of best has changed, here's my list:
1. Led Zeppelin - probably 1972? (they were starting to play some songs from the Houses of the Holy album, but it hadn't been released yet) - at the old Chicago Stadium.
2. Luther Allison (blues guy) at a little club in Champaign, IL, probably 1976 or so). Kept playing for an hour past closing. When he broke two strings on his guitar, he switched to harmonica. Had his bass player carry him on his shoulders around the club, and then started jumping from table-top to table-top.
3. Cheap Trick, also at a small bar in Champaign, after hours.
4. The Who - one of their first "last tours". OK, this was after Moon died, but I never saw them live before. It was at Alpine Valley, in Wisc., an outdooor venue normally suited to 20k people or less. But there were 40k people there, and the grassy hill was a sea of mud from heavy rains. Plus, the rest-rooms overloaded, and were ankle-deep in whatever. But the Who led off with about 45 straight minutes of Tommy, and never let up. The atmosphere was highlighted by the presence of lots of Dead-heads who had stayed over from a Dead concert a few days earlier. I had never seen people twirl in place for so long!
5. ELO, just before they became known. This was prior to the release of their "Roll Over Beethoven" single, so probably around 1971? It was out the Dupage County Fairgrounds in Wheaton, IL - not even at the main fairground stands, but in the little building where they usually put some of the 4H exhibits. The stage was like a typical high-school or church "fellowship hall" stage - i.e., about 3 feet above the floor level. No seats, just sit on the floor or stand. I had no idea who ELO was, only that it was only $2 to get in. They started out with "In the Hall of the Mountain King", and everyone just stood there with their mouths open while the violinist and cello player jumped around in their black suits, capes, hoods, etc.
As you can tell, a lot of my favorite concerts were from seeing bands in small venues, either before they got famous, or "after hours".