The more I play tile-based strategy games, the more enamored I am of hexagons. Both from the player perspective and the design side. Player-wise, they're awesome because they retain visual distance correctly. Some grid based games try to even up moving diagonally by making it more expensive, and some don't. Sometimes you forget which is true in a game you're playing.
From the design perspective, hexagons are awesome because there's very little work that needs to be done, data-wise, to implement hexes. In the simplest case, a simple conversion rule lets you use a normal 2d array and you just "ignore" the data points that don't fit into a hexagonal grid. Hexes make range calculations much more simple, from ranged attacks to movement to area-of-effect.
So, being that I prefer one so heavily, what's the problem? Other people, naturally. As I'm finishing up the prototype for Conquer the Castle, I'm toying with the idea of switching to hexagons when I move into the creation of the final product. But I have this anecdotally-supported idea in my head that the average player finds hexagons confusing, and prefers a square-tile grid. I'm wary of "aiming for the largest possible audience," but that doesn't mean I want to shoot myself in the foot by discounting a lot of players who might otherwise try the game.
Guess it's audience research time.