One of the things that I really like in a game is the ability to choose how I play it. In any good sandbox game a player can typically get side-tracked for hours just goofing off. I like that. I can spend that kind of time running from the police in any GTA game. Let's say you grab a motorized shopping cart in the parking lot and you have some good laughs running into people and just driving around? Open-ended gameplay is one of the many addicting factors in a game. I've even been guilty of running an in-page search of an article on a game I'm thinking about getting to find key words like sandbox and open-ended. Of course sandbox and open-ended are not the same thing, but they both are heavily defined by the players ability to choose.
The Sandbox