I watched a class (a single 2 hour lecture I believe) taught by Conway at Mathcamp. It was about, believe it or not, the simple game of dots-and-boxes - except that Conway had attacked it with a lot of math and derived some strategies for winning. He was indeed a great lecturer, even though he was quite old.

The most memorable part was right at the beginning where Conway asked someone to play a 4x4 grid of dots and boxes with him 10 times in a row. As I remember, Conway won 9 times in a row. That got all of our attention! :)