In case myimage.gif isn’t transparent, you could use multiple backgrounds:
background: url('myimage.gif'), url('fallback.gif');
This way fallback.gif will only be visible if myimage.gif isn’t available.
Note that fallback.gif may be downloaded even if myimage.gif is available.
Alternatively, even though not widely supported, CSS Images 3 introduces the image() notation:
background: image('myimage.gif', 'fallback.gif');
Multiple
<image-decl>scan be given separated by commas, in
which case the function represents the first image that’s not an
invalid image.