It depends on your screen size and resolution how you see the background, but you also have to consider that there is many other size screens too. I've took these screen prints with both of my computers. You can see, that there is quite much difference.
Here you see this blog with 1680 x 1050 resolution in 22 " screen.
And this is the same blog with 1024 x 800 resolution in about 15 " screen (my laptop). You can go and check how you see it, this is my Kyynelkaasua blog. It is a normal 2 column Minima template.
Here is a 3 column Minima template in 1680 x 1050 resolution in 22" screen.
And same template with 1024 x 1024 resolution on my laptop 15" screen. How you see my other blog, go and check here.
I make all my backgrounds on 1600 x 1200 px size, some older ones are 1450 x 1100 px. So they all fill the screen even with larger screens. In smaller screens you don't see everything, but I try to place the main images so, that the main parts of them are also seen on smaller screens. I check my backgrounds with both of my screens.
Sometimes I see backgrounds which are too small for bigger screen or too large for the small ones. I recommend to make the background large enough, but make sure if you have images there, that you place them right, that you can see the best parts of them also on the smaller screen.
It's quite difficult to explain, specially for me in English, it would be much easier for me to write in Finnish, but I bet that most of you would not understand a word. Feel free to correct my English anytime you see something written wrong. ;)
And feel free to ask anything about background making, I try to answer as well as I can.