CSS background image to fit width, height should auto-scale in proportion

There is a CSS3 property for this, namely background-size (compatibility check). While one can set length values, it's usually used with the special values contain and cover. In your specific case, you should use cover:

body {
    background-image:    url(images/background.svg);
    background-size:     cover;                      /* <------ */
    background-repeat:   no-repeat;
    background-position: center center;              /* optional, center the image */
}

Eggsplanation for contain and cover

Sorry for the bad pun, but I'm going to use the picture of the day by Biswarup Ganguly for demonstration. Lets say that this is your screen, and the gray area is outside of your visible screen. For demonstration, I'm going to assume a 16x9 ratio.

We want to use the aforementioned picture of the day as a background. However, we cropped the image to 4x3 for some reason. We could set the background-size property to some fixed length, but we will focus on contain and cover. Note that I also assume that we didn't mangle the width and/or height of body.

contain

contain

Scale the image, while preserving its intrinsic aspect ratio (if any), to the largest size such that both its width and its height can fit inside the background positioning area.

This makes sure that the background image is always completely contained in the background positioning area, however, there could be some empty space filled with your background-color in this case:

cover

cover

Scale the image, while preserving its intrinsic aspect ratio (if any), to the smallest size such that both its width and its height can completely cover the background positioning area.

This makes sure that the background image is covering everything. There will be no visible background-color, however depending on the screen's ratio a great part of your image could be cut off: