Having a favicon for your domain name will not currently help your search engine rankings. But it does have indirect benefits that might, in the long run, benefit your site's rankings. This is the topic of a threat at SEW Forums named Is there any SE benefit to using a favicon.ico file?.
A favorite icon (favicon) is the small little graphic displayed to the left of the URL in the browser's URL bar. For Search Engine Watch it looks like 
for this site it looks like 
and for my corporate site it looks like 
. So how can this favicon help?
(1) Makes your site standout from the others (since many still do not have favicons). (2) The extra branding might help you get more links to your Web site, helping with search engine ranking. (3) On some browsers, that have "tabbed browsing" (Firefox, Ssafari, Netscape), it helps identify which tab has which site in it. (4)Keeps your error logs cleaner
