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Life was invented by John Conway, and has simple rules:
1) A cell lives if two or three of the surrounding squares are occupied.
2) An empty square has a cell born in it if three of the surrounding squares are occupied.
3) The states of all cells are determined simoutaneously.

Life Applet by Andrea Gilbert.

Martin Gardner has written 3 articles about Life; all of them are highly recommended.

Andreas Ehrencrona has written an excellent page about John Conway's Life.  It includes several nice Java Applets.  It also includes a very nice cellular automata applet.  Source code is included.

Alan Hensel has written an excellent Java Applet here. It inculdes a large online library of Life forms.  Also on this page are links to many other nice Life programs.

http://www.radicaleye.com/lifepage has many Life links.

Sante Fe also lists a number of nice Artificial Life Programs that can be downloaded.

Stephen Wolfram, creator of Mathematica, wrote many excellent pages about cellular automata here.

David Eppstein also has written many pages about cellular automata, some of it contradicting Wolfram's papers.

I will expand this page if I ever find a way to top the pages above.

The Collection of Java CA Applets has dozens of Cellular Automata Java Applets.  This is a nice site for getting the breadth of the field.