This really depends on what your background image is. If it's a gradient that goes say from blue to white then set your background color to white, make the image 1 pixel wide by whatever height is required to complete your gradient and then set the background image to repeat-x and the background should be fine irregardless of the screen resolution.
If it's more complex then a gradient you should look to making it into a 'tile' that can be repeated on both the x and y axis (as small as possible) and again that should sort you on all resolutions.
HTH,
JC