It amazes me how far Conway's Game of Life has come over the last 3 decades. I remember playing it by hand with pencil and graph-paper when I was at school!
Have a look at Paul Callahan's Patterns, Programs, and Links for Conway's Game of Life, especially the awesome Life Pattern Catalog. It is incredible what complex machines can be constructed from the starting point of three very simple rules. Life nimrods are even working on a Turing machine. Imagine that - a computer running a game that contains a simulation of a computing machine!!