How to remove file versions from the file source links in wp_head?

You can hook into style_loader_src and script_loader_src and run remove_query_arg( 'ver', $url ) on the URL:

<?php
/* Plugin Name: Remove version parameter for scripts and styles */

add_filter( 'style_loader_src', 't5_remove_version' );
add_filter( 'script_loader_src', 't5_remove_version' );

function t5_remove_version( $url )
{
    return remove_query_arg( 'ver', $url );
}

Without this plugin:

After plugin activation:

There is one case where that will fail: When someone didn’t use the script/style API, but added a hard coded string to the header.