Billy Joel/Awesome

Billy was known to be extremely physical on stage during his live shows, frequently doing flips and handstands off the top of his piano, as well as spinning himself around and climbing up the stage. He still jumps off his piano in his 60s, albeit to a lesser extent.
The famous stunt at the 1994 Grammy Awards. After Frank Sinatra was "played off" during his Lifetime Achievement Award speech, a pissed-off Joel extended the break in the middle of "River of Dreams" to upwards of a few minutes in revenge, to the approving laughter and applause of the other stars in the audience.

"Valuable advertising time ticking away. Just ticking away. Dollars... dollars... dollars. [sits there in silence with the biggest cat-canary grin]."

The shows he did at Shea Stadium in 2009 - the last concerts ever performed at the venue - certainly qualify, particlarly one major coup pulled by him and his crew. About halfway through the final show, they got a call from Paul McCartney (who'd previously said that scheduling conflicts would prevent him from appearing) who explained that he was on a plane coming into New York and asked if Joel's invitation was still open. The crew proceeded to arrange for a runway to be cleared for him to land and got him a police escort to the stadium, where he triumphantly emerged onto the stage to perform "I Saw Her Standing There" with Billy's band.
On January 30, 2013, Joel was the guest at "An Evening of Questions and Answers" at Vanderbilt University, when a student in the audience asked if he could perform "New York State of Mind" with Joel. He said "Okay." The result was beautiful.