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?
you can use the __utm.gif tracker without javascript (w some server help)
you can use it in an email message (w some programmatic help before sending the email)
Urchin was developed before AJAX was popular (2005)
It has nothing to do w cross-domain. They could have used JSONP for that.