How To Remove WordPress Version From The Admin Footer

Add this to your functions.php:

function my_footer_shh() {
    remove_filter( 'update_footer', 'core_update_footer' ); 
}

add_action( 'admin_menu', 'my_footer_shh' );

or, if you’d like to hide it from everyone except admins:

function my_footer_shh() {
    if ( ! current_user_can('manage_options') ) { // 'update_core' may be more appropriate
        remove_filter( 'update_footer', 'core_update_footer' ); 
    }
}
add_action( 'admin_menu', 'my_footer_shh' );