web config is a great little place to store global parameters such as:
database connection params
admin email settings (smtp, admin email account...)
where to log errors to
even role based authentication XML parameters

many other web languages have used a config file (such as java's web.xml) for many years, so it's about time MS caught on.

you can run the site without the web.config, but if you use something that requires params from it, it'll kick an error the first time and say "I need to create this file for you before you can proceed"