one of the least enjoyable feelings I have had on stage is feeling like I am being "careful," in order not to do something wrong. The truth is that the kind of music I play requires quite a lot of concentration and preparation, and of course I always want to do my best, technically and expressively. But I know that the most successful performances, given by me or by anyone, are the ones that leave nothing left in the tank. In classical music, we are perhaps more likely to lose sight of the need for "abandon" because the technical demands (and at times the memorization demands) are so great. We need to be in total command of the notes and other aspects of the music before we can really "let go" of course, and it doesn't take nearly as long to reach this point of "command" in playing most types of popular music. Here is a video of Queen performing "Bohemian Rhapsody" - Freddie Mercury and the rest of the band are playing like their lives depend on it, and that is something all of us in classical music should aspire to in every performance:
It may help when you are the composer of the music you are playing - you can inhabit the music and feel free with it in a way that is harder to achieve when you are playing someone else's music. However, not only is Astor Piazzolla wonderful playing his own "Milonga del Angel", so too is the violinist in his group, Fernando Suarez Paz:
Finally, the one pianist I know who most consistently achieves this ideal of total control making possible the appearance of total abandon, the incomparable Martha Argerich, playing the 1st movement of the Prokofiev 3rd Concerto:
I can say that I remember two times in my life actually bleeding on the keyboard during a concert, once during a performance of the Ravel Left-hand Concerto (after a bunch of glissandi, which do tend to rip up one's skin) and once during another piece by Ravel, Gaspard de la Nuit, in a concert somewhere in Northern Ireland. I'm not sure how that one happened. I have also once played the Bartok 2nd Concerto with a fractured finger but I can definitely say I didn't really play with "total abandon" that time.