I'm making a game with XNA, what I'm wondering is; what should the dimensions in pixels be of the window? It needs to be a size that will work on the majority of computers. I'm not sure if there's some size that most games use.
On a PC or the Xbox 360, there's no single size that is "best", or that all games tend to use. (The Windows 7 Phone has far fewer choices.)
There's no reason to not use the native window resolution by default.
In XNA, you can do this with code like this in the
Of course, it would be meaningful to provide the user with options to change the size they are using, as ChrisF points out. Many people may not ever use it if you've chosen a good default. Still, though, it's one of those things that makes a big difference for the people who want it, and it doesn't take a whole lot of work.
You can also find a good list of common screen resolutions on Wikipedia.
Your biggest challenge in this area will be writing your game in a way that it can handle a wide variety of resolutions and aspect ratios. This is especially true if you want to run the same game/codebase on the PC, the Xbox 360, and the Windows 7 Phone, all of which, XNA supports. From a technical standpoint, here's a few things you can do to help address this problem:
Use scalable assets when possible, and use the full resolution of the screen. There is no reason to require a user with a large monitor to be stuck with a 1/4 screen window due a limit of 800x600 screen size. I have specifically dropped games, despite promise in their gameplay, if I cannot play them fullscreen and at my native monitor resolution.
A better question might be aspect ratio. This is a harder one, because the majority of screens are now 16:9 or 16:10, but there are still a lot of 4:3 monitors out there. Adjusting the aspect ratio of a game is more difficult than simply scaling the UI, as it requires dealing with anchoring and whitespace. If you cannot make your user interface adjust to multiple aspect ratios, then you should allow the screen to letterbox as needed when the screen ratio does not match your game UI ratio.
Make it configurable or user selectable, and allow the user to maximise the window.
There's no need in a modern game to restrict the size of the window the user can play the game in.