Detect linked & unused files and unused JavaScript
I had this need so I created a tool that detects unused JS on the browser side, not just from the sources, so it can also test third parties scripts.
It works by creating a local proxy on your computer that intercepts JavaScript requests and instruments these files on-the-fly. The tool is than able to detect which parts of the instrumented files have been used by the page, and which don't.
I made it open-source and you can find it here: https://github.com/gmetais/unusedjs.
This answer offers Google's Closure Compiler which, in the process of minifying and concatenating your JavaScript code, can remove "dead code".
Quoting from the documentation for the compilation levels:
Compilation with ADVANCED_OPTIMIZATIONS removes code that is provably unreachable. This is especially useful in combination with large libraries. If you use only a few functions from a large library file, the compiler can remove everything except those functions from its output.
Also see this answer which contains more information on Google's Closure Compiler.