HereForTheBeer: Whenever "sandbox game" is mentioned, I always think of the building games like SimCity, Railroad Tycoon, etc. You know, build stuff, like in a sandbox.
A sandbox game is one where you are supposed to make your own fun. The game provides you with a lot of tools to play with, but in the end, the players enjoyment will be based on how good the player is at entertaining itself.
For me, the ultimate sandbox game is
Dwarf Fortress. Not even The Sims offers you so many different ways of being a jerk to everyone of your "minions" (Yes we really did intentionally drop your kittens down a bottomless pit, what are you going to do about it? Sulk in your room?).