OK, here we go, I'll try to remember them all, at least the good ones:
George Thorogood and the Delaware Destroyers (1980 or so, 1984, 1989) - also saw George, unplugged and alone, at a party.
James Brown (1981) at age 45 or so, he played a 2-hour set with microscopic breaks between songs, and I don't think he had both feet on the ground for more than 10 seconds at a time.
Moody Blues (1981 or so) - my girlfriend of the time really loved them
The Who (1982) - the first of many "we're never touring again" tours.
The Clash (1982) - didn't live up to its potential.
John Lee Hooker (1982 or so) - an amazing, free show in a park. Maybe 200 people there. I could have polished his boots from where I was standing, and would gladly have done so.
Billy Idol (1984 or 85) - more fun than it had a right to be.
King Crimson (1985 or 86) - They can not only play like that for the recordings, but they can repeat it live - and probably backwards, if the urge struck them. An absolutely breathtaking performance.
The Replacements (1990) - I didn't know you could be that drunk and still play an instrument, no matter how badly.
INXS (1990) - not a bad show but not spontaneous enough.
Elvis Costello (1991) - an excellent show in which he played not one popular song, and most of which I'd never heard, despite being a long time fan.
Ned's Atomic Dustbin/Jesus Jones (1991 or so) - not bad show, a small venue and they managed to blow the power main in the middle of it.
Then we had kids so there is a bit of a drop-out.
They Might Be Giants (1994, 1996 or so, 1999, 2001, 2002) - one of the great live bands of all time. You never know what they're going to hit you with - odd takes on their own songs? A "battle of the band members" improv contest? A six-minute medley made up of 20 or so individual songs that are only 10-15 seconds long? A cover of "Frankenstein", or maybe "Hey There Georgie Girl"? A polka? A voice-mail drum solo? Miking a radio through the PA, spinning the dial at random, and playing along with whatever song tunes in? I've enjoyed every second of their shows when they are on stage.
Nine Inch Nails (2001) - also a truly great show, visually stunning, excellently played; Trent's still got it and lots of these new upstart punks really wish they had it too.
This isn't counting all the various opening acts, etc. that were pretty forgettable.
My wife dunks over me in concert attendance, though, because she grew up in New York. With easy access to Madison Square Garden throughout the mid-to-late 70s, she's seen:
Pink Floyd - Animals tour, with the giant pig.
Led Zepplin - yes, the real Zep, with Bonzo drumming.
Oh, cheez, I know she's seen alot of other great bands; I'll have to ask her.
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, so between the two of us, we have one complete, well rounded individual... How lucky are we, eh? 
