The advantages of using other people's feeds are obvious, but what about supplying your own? There are at least eight reasons to do so:
It increases traffic to your site.
It builds brand awareness for your site.
It can help with search engine rankings.
It helps cement relationships within a community of sites.
It improves the site/ user relationship.
With additional technologies, it allows others to give additional features to your service update-notification via instant messaging, for example.
It makes the Internet an altogether richer place, pushing semantic technology along.
It gives you a good excuse to play with some cool stuff.
There you are: social, spiritual, and mercenary reasons to provide an RSS feed for your site.