Wordpress - 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.

This worked for me when I still had to load a stylesheet from Google Fonts.

<?php
add_filter( 'script_loader_src', 'wpse130419_remove_script_version', 15, 1 );
add_filter( 'style_loader_src',  'wpse130419_remove_script_version', 15, 1 );
function wpse130419_remove_script_version( $src ) {

    $url = explode( '?', $src );

    if ( $url[0] === 'http://fonts.googleapis.com/css' ) :
        $version = explode( '&ver=', $url[1] );
        $url[1]  = $version[0];
    endif;

    return ( $url[0] === 'http://fonts.googleapis.com/css' ) 
        ? "{$url[0]}?{$url[1]}"
        : $url[0]
    ;
}