What happens to my blog when I graduate?

From Help Wiki

How to manage your Wordpress site after graduation

Once you graduate your blog will eventually be disabled.

The deactivation process happens in mid December and disables any blogs that do not have an active Evergreen login associated with them. The sites are then permanently deleted 3 months later at the beginning of Spring quarter.

Can I take it with me?

Yes. Export it. You can use the built-in export feature to export your site to Wordpress.com or to other blogging services as well. See Exporting Your Blog for instructions. Keep in mind that you won’t have access to the same plugins and themes that are available at blogs.evergreen.edu. Another alternative to consider is to get your own domain name and host your own Wordpress installation. Several web hosts provide pre-installed versions of Wordpress and make it pretty easy to get up and running. With your own Wordpress instance, you would be able to install any plugin or theme you wanted.

See: http://wordpress.org/hosting/ for a list of recommended hosts that provide easy Wordpress hosting.