Here's mine. Feel free to expand on this one and suggest changes, in addition to posting your own game types.
Treasure Hunt
This idea was, obviously, pirate-inspired and is pretty simple.

An additional idea would be to add a dummy treasure. It's not buried, but otherwise looks exactly like the real one and still causes a "Team *blank* has the treasure!" message to be displayed. Once you have the dummy, your team recieves a message letting them know it's a fake. I don't know if this particular idea has actual merit, and would add anything to the game. Just seemed like something worth throwing out there.