Dead Rising is a good example of a fairly unique game available for the Xbox 360. Sure, there have been zombie games before. And there have been camera games as well. But Dead Rising combines these two features, along with the always-satisfying ability to destroy zombies in various different ways, in a humorous and captivating manner.
In the Dead Rising scenario, you are trapped in a shopping mall along with several other people, and your goal is to survive 72 hours. Naturally someone screws up and lets the zombies in, and you have to avoid, confront, and take pictures of zombies (you're a journalist, after all) in order to survive. There are many situations in which you can find zombies that could be picture worthy. Perhaps you'll see some zombies falling off roofs, pushing shopping carts, or eating someone's innards. Surviving while you put together a Pulitzer-worthy portfolio of zombie photos is pretty much what you do in this game.
Dead Rising is not, however, an entirely open-ended game. There are many goals you must meet in order to solve various "cases" which is just another way to say figure out things that are worth reporting. It is actually pretty challenging to get past some of the cases where you must fight difficult enemies, and sometimes the controls can be pretty unnatural feeling.
Nevertheless, it's still fun to go back and try to find all the different items in the environment that can be used as weapons (some are hilarious but quite ineffective), and hone your zombie-fending techniques. What's more, even if the game is difficult for you (as it was for me), at least when you die you get the chance to start over at the same character level you left off at, making it much easier the next time through.