the greatest Rat Pack Sammy Davies Junior, Dean Martin and Frank Sinatra

Youssou N'Dour & Super Etoile De Dakar
Baaba Maal
Les Yeux Noirs
Radio Tarifa
Neil Young
Clannad
America
Yothi Yindi
RS, Pink Floyd, U2 used to make the biggest show on the biggest stage. Quite impressive.
However, one of the best surprises I ever saw was George Clinton.
I am not sure about best or what, but the most fun I had was at the V Festival a few years ago when the Scissor Sisters were performing and Franz Ferdinand came on stage. Followed by some weird inflatable muppet looking characters.
I am struggling to remember the name of the band a few years ago that used to use those kinds of muppets/puppets but they were similar ones used by the Scissor Sisters.
I have probably been to others that I liked more, but that was fun.
Oh, I fell asleep at a Smashing Pumpkins concert when I was 16. That was memorable.
I wouldn't say it was the greatest, but I was knocked unconcious by a beer can (full) at the Red Hot Chili Peppers concert at Hyde Park. Not the best live act but again, it stood out.

Springsteen 1979, Lynard Skynard 1976, Robert Randolph and the Family Band any time they play.
Every single time I see them, I think its nine or ten times now, they are absolutely mindblowingly exceptional: Wilco of course.

Ornette Coleman
the first time i saw Godspeed You Black Emperor
Mazzy Star
Melt Banana
Beck back in 1999
Low in a church in amsterdam
The Afghan Whigs
Suicide in a private party in London
Primal Scream with 100 people at a studio in London
Bardo Pond
Portishead in LA back in 1999
The Boredoms at the Scala
Soul Junk
Sufjan Stevens before he added all the bothersome trumpets and twang.