BuddyPress.org

Single WP install, sure. Just add the categories from backend and users can only choose from the available categories.

If you’re talking about categorizing a multisite blog, you could use something like this https://wordpress.org/extend/plugins/blog-topics/

Or if you’re looking to create categories in main site which are automatically added to new subsites of multisite install http://wordpress.stackexchange.com/questions/12201/wordpress-multisite-global-categories