I really like Ben's answer, but I wanted to add my two cents:
Like Ben and others have mentioned, Conway's Game of Life provides a "wow" factor that's useful in and of itself. It's simple to understand, and easily leads to pretty patterns and cool animations. This inspires students to want to play around with the code, which by itself is pretty valuable.
On top of that, it leads to some pretty interesting more advanced topics, such as:
In philosophy, systems theory, science, and art, emergence is a phenomenon whereby larger entities arise through interactions among smaller or simpler entities such that the larger entities exhibit properties the smaller/simpler entities do not exhibit.
Emergence plays a central role in theories of integrative levels and of complex systems. For instance, the phenomenon of life as studied in biology is an emergent property of chemistry, and psychological phenomena emerge from the neurobiological phenomena of living things.
Imho, emergence is one of the coolest things about computer science.
From emergence, you also get to talk about swarm behavior, including programs like:
The list goes on, and the related articles at the bottom of all of the above are a vertiable black hole of fascinating stuff.
Artificial life (often abbreviated ALife or A-Life) is a field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations with computer models, robotics, and biochemistry.
From here you can talk about artificial intelligence, neural networks, machine learning, etc.
The Game of Life is just one example of a cellular automaton. There are a ton of other examples.
You could use a 1D cellular automaton to introduce the concept to less experienced students.
The game of life (and other cellular automata) also has practical applications, such as being used in simulations of bacteria, epidemic / disease outbreak, and forest fires.
Do a search for "cellular automata forest fires" or "cellular automata disease modelling" for a ton of results.