The important thing is not really about how big the background should be, but what screen size are you designing for.
Here is an article about how screen sizes are getting bigger as the old CRT monitors are finally being left in the dust in large numbers. You can see by the pretty chart in that article that larger (1280 - 1600 wide) monitors have now become the majority, leaving 1024 - 1152 to slowly shrink away.
You also have to consider who your audience is. It is no secret that younger, tech-savy users will be on the larger end of the screen size, while older, pre-Internet generations who only check email, browse some basic sites, check Facebook and occasionally play casual games fill out most of the smaller screen portion. If your content adds in hobbies that center around the computer or technology, such as computer builders, PC gamers, etc., to your userbase, the percentage of your audience on large monitors goes up even higher, with probably most if not all clocking in in the 1280 - 1600 group.
I say, particularly for games, to take a chance and go bigger on your designs. Many popular sites today that are still designing for small monitors look comical on a large monitor!