Of course, different cellular automata have different rules for generating the next generation, and even different grid structures. Conway's game of life is the most well known mainly because the rules are so simple and yet the outcome is so complex. In fact, the outcome is so complex that the only way to predict it is to actually run the simulation.
What's the educational value of Conway's game of life? NLVM has a good exercise that allows students to become familiar with the rules of game, but this is nothing more than a simple counting exercise. The value in working with these simulations can provide so much more insights for curious students. For example, it is a very complex puzzle to engineer life patterns that repeat themselves, move over time, or remain stable. It's instructive to ask: “What kind of stable patterns emerge from these rules?” This requires some playing around with a simulator, as well as some high level reasoning. Another good question to ask is “How long does it take for a pattern to stabilize and is there a way to predict it?” Due to the nature of the game, that question can't be answered exactly, but it can be answered inexactly which requires a type of thinking that is relevant to real-world problems. Given current technology trends, this type of thinking is becoming increasingly important.
A lot of life simulators exist online — in fact Wikipedia says that there are “thousands”. We've looked at many of these, and will report on some of the interesting ones.