Yes, you should break up your javascript files into relevant parts just like you break up your php files into relevant parts. The one key factor here is they should be combined and minified before being served up to the browser so the user does not have to make several network calls to your server for each .js file.
Check out Google Minify for an easy solution to that issue.
Take a look at the JQuery source to see how they divvy up their files. Now look at their combined framework, and of course their minified framework. What is actually served up to the user looks nothing like the source.