HTML: Background image of website should not scroll with the rest of the page

Just use the following CSS to implement your plan:

body {
   background-image: url("background.jpg");
   background-repeat: repeat-x;
   background-attachment: fixed;
}

The property "fixed" provides the effect that you want. The "repeat-x" is favorable at this point, if you have an image that should be repeated across the top of the page from left to right (for example, a shadow or something similar). If you would like to have only one image without repetition, you have to omit the "repeat-x" or you can use another "background-repeat".

Example: the website sttmedia.com is using exactly the code above with "repeat-x" and "fixed". There, you can see how this is looking like.
2012-06-03 at 04:40