There is a game called Zombeja! Ovella!. This game, of which my friend owns a limited, hand-crafted collector’s Edition, is a roleplaying game with a game board. Not a battle grid, but an actual game board. Containing the starting point and the finishing line.
The purpose of the game is to survive a zombie infestation. The players start in the middle of the board, and the zombies (or an allegory for a zombie invasion. Like communism) start at the other end. Each step describes the magnitude of the zombie invasion: At the start of the game, they are just some rumours on the news. And at the end, they are unstoppable and have developed some new abilities. The purpose of the players is to get to the other end before the zombies move over their marker. Each turn, a new player describes the next scene. Then the players roleplay what their characters do. If they have a conflict, both players roll a die, and the winner steps away from the zombies, and the loser towards them. At the end of the round the zombie marker moves closer. Every player who gets to the last square on the game board escapes unharmed.
I like the game. It is short, it can be funny or serious and most of all, it is structured. The game has a distinct beginning, where everyone arms and the threat of the week is described, a middle when the players try to escape via conventional means and an end, when the frantic despair engulfs the last survivor(s). The game board idea is quite clever, and a very convenient way to telegraph the intended mood to the players. I actually would like to have such a tool to aid me in the games I play. I could imagine my Pathfinder campaign using a game board: Every 5 days, a new event happens somewhere on the map. I roll for the place and the entity that causes the trouble. Then, as the players travel towards the place, I would write the details up and be prepared with another adventure.
The reason I haven’t used such a system is because the rules do not enforce it. The game rules are just concerned with simulating the world, not the narration. Zombeja! does.