Why does Google Analytic request a GIF file?
Is it because the GIF allows access to more data than JavaScript alone. Is it to get the IP address of the user?
Even with JavaScript enabled, analytics requests a GIF file. If you look at the GET params of the image, it contains a lot of information about the browser. Stuff like utmsr=1280x1024 (the screen size). Google Code has a list of parameters.
It uses the image request to send information about the browser without an XMLHttpRequest.
Now, to actually answer the original question, Google is probably doing this to get around cross-domain XMLHttpRequest restrictions.