I think one of the best was the long-running MTV UNPLUGGED which won numerous awards both for the program and various artist who participated over the years.
One of the most memorable was Eric Clapton. Even tho he had released it on cassette, it was his first public performance of Tears in Heaven. This is the song he wrote following the tragic accidental death of his four year old son falling out the window of the 50th floor apartment of a friend.
MTV Unplugged has its own YouTube channel with loads of clips. His is one of the few shown in its entirety. Its a beautiful performance.