There's a story about Artur Rubinstein playing the Chopin E minor concerto, a piece that he'd performed constantly since the age of 17 or 18. Anyway, at this time he was at some time in his middle life and in the first movement, he shocked the audience by literally pausing in a solo part because he forgot the music; he "flubbed around" for two or three minutes (the conductor and orchestra was clever enough to help him cover the mistake up, I believe) and then, when he finally found the cue, came back in perfectly and performed the rest of the concerto flawlessly, and to a standing ovation. However, he felt so bad about it that at the ultimate end of the concert, he had the orchestra rearrange itself and they performed the first movement again after Rubinstein apologised deeply to the audience.
There is also a story of him playing the wrong Hungarian Rhapsody because moments before he exitted the backstage area to go play, his children were humming A Hungarian Rhapsody but not THE Hungarian Rhapsody--so, yeah, he played whichever one they were humming and the audience spent a good amount of time checking their programs and wondering why he'd made the change, heh. After he finished, he suddenly realised the mistake and warmly apologised, then played the proper Rhapsody.
As for me...well, I've made too many performance mistakes to count. Usually I just try to take the opportunity and improvise my way back in, but that goes poorly if I'm playing Mozart because, well, I think that speaks for itself...so, yeah, when doing something that I don't particularly know well or that's in the Classical era, the improv technique doesn't work and I end up repeating an awkward section or something of the sort. If it got to the point where I could no longer play, I'd take out the music if it were handy and then formally address the audience about the issue, apologising and maybe even trying to appear charismatic by asking them if they wish me to continue (heh, my typical audience could probably swing anyway indifferently...)