Getting a stack trace when an error occurs?

I was told to “get a stack trace” when an error occurs in my WordPress installation. How do I do this?

This is meant to be an easy place to refer others to. Please list plugins, configuration settings, PHP modules… that can do this. Consider that the user might be on a shared host, might want to log to a file instead of the browser, …

Maybe you are after something like WP PHP Console.

Another good plugin would be the Simple Error Handler, while it should be regarded it is compatible only up to 3.8.11 and you may consider forking it to be compatible to latest version of WordPress.