In Drupal 7, how do I allow users to see their own unpublished content?
view own unpublished content permission allows just that - to see /node/%nid even if it is unpublished. Test it, I'm sure it will work.

If you want your users to be able to list their content, well, that's other topic. Easiest way is to use Views to create listings filtered by authors, with filters like is_published or author == current_user).