Whenever you have an auth system like the first commenter said.
Wiki's could be cached. Forums shouldn't be cached if they are fairly active as you want your users to see the fresh content every time they visit
Also watch out for flash messages. As an example a user fills out a form and you flash "Success thanks for registering" when you render the home page. You wouldn't want that message to appear to the user the next time he visits your page.
Watch the Railscasts Dynamic Page Caching episode for lots of great information and potential problems you may run into. http://railscasts.com/episodes/169-dynamic-page-caching-revised