If the image is a jpg, then it may have been saved in a problematic "sub-format". JPG is a kind of junk drawer, rather than just one thing. The best bet is using Photoshop and then "Save for the Web".
Also, look at the CSS rule that declares the background image. IE may be forgiving some kind of syntax problem that FF is more strict about. You can use the W3C Validator for CSS [jigsaw.w3.org] to surface possible problems.
[edited by: tedster at 6:47 pm (utc) on Jul 10, 2010]
Thanks Ted I'm going to start looking at these things right now. I did indeed, create the BG image in Photoshop (CS4) but I don't remember if I did the 'save for web' thing or if I just saved it as a JPG.
Yep it was the CSS file. Dreamweaver created a relative link to the BG image file for some stupid reason. So the browser was looking for url(file://c:\WebDesign\blah, blah, blah) instead of just /images/filename.