To some people, this is proabably obvious, but for the rest of us, it took some digging, but I found how to have a different single.php file for each post type.
I thought it would be good to share it here, in case anybody else is looking for the answer.
Firstly, for those post types that will just use the default look and feel, you don’t have to do a thing. For those wanting to do something a little different with each post type, or selection of your post types, you’ll find the answer ridiculously simple.
Take your single.php file and rename it, using the post type name. So, if you have a post type called books, you would rename your file single-books.php.