I want to use a background image like the one below as the background of a site. The problem is, I don’t want it to tile. I want the top edge to be the top edge of the window, side edges to be the side edges of the window, and bottom edge to be the bottom edge of the window. The middle portions, both horizontally and vertically, should repeat in a natural looking way to fill up all the space, making it appear that the paper is the size of the browser window. Is there a good way to do this?

I would use something like this: http://srobbin.com/blog/jquery-plugins/jquery-backstretch/ ( Note that this is not the only background stretching script ) Upside with these is that it keeps the aspect ratio of the image.
Dunno if keeping the aspect ratio is necessary or even desirable in your case..?
IF i wanted to go all extreme on this background i would:
site bg.
repeating them to whatever direction is needed
If i had all these elements in their own layers. Though that wouldnt be hard to fabricate.