In Windows Phone 8 you are able to save a screenshot by holding both the power button (often on the side of the phone, between the volume buttons and the camera button) and the home button (the middle button under the screen, with the Windows logo on it) for some time. Such screenshots are saved in the Screenshot album of the Picture Hub.

And just to be complete: in Windows Phone 8.1 Preview this combination was changed to holding both the volume up and the power button. If you use the older Windows Phone 8.0 key combination, you get shown a message box that tells you of this change.

For normal users (no developers) in Windows Phone 7.5 and earlier there is no way to make a screenshot of your phone except using another camera(phone) to do it. I think this is still the case in the Windows Phone 7.8 update that brings the smaller home screen tiles from Windows Phone 8.