Conway's Game of Life
In particular, I knew the biggest problem for writing this in JS would be in rendering performance time, especially if we are relying on the DOM for each cell element. So, the challenge lay in not so much writing the program, but how to make it performant in the browser.
So, here's what I came up with. You can run this at my website http://arei.net/dev/GameOfLife or download the source code and open it on your own local machine.
Also, if you want to take it out and make some tweaks, see if you can get better performance, I'd love to see your fork. Let me know!