Here I've adapted Conway's algorithm to a hexagonal grid where each cell has six neighbors. The original three/two rule doesn't produce very interesting results with this configuration. In fact, to get something that propagates in much the same fashion as the original game, neither exploding out of control or dying off too soon, I had to come up with a set of rules that takes into account not only the six immediate neighbors but also the six 'second tier' neighbors that form the points of a star of David. This set of rules is described here.
You can load one of several predefined starting patterns with the Load button and the drop-down menu box, or you can experiment with your own starting patterns by clicking directly on the cells. Clicking the Go button starts the simulation. When game is running, the go button turns into a stop button. The simulation can be sped up or slowed down via the slider at the bottom. Activating the Wrap checkbox causes the "playing field" of the game to wrap around across opposite sides.
As far as I know, no one else has come up with a hexagonal version of life. Admittedly, I've only researched this to the point of following lots of links from Life web pages.