Removed jQuery script from header.php , any problems?

Here is the correct way to include jQuery in your theme.

Open functions.php in your theme folder and add this to it:

 // Proper way to enqueue scripts and styles
    function royal_insert_jquery(){
    wp_enqueue_script('jquery', false, array(), false, false);
    }
    add_filter('wp_enqueue_scripts','royal_insert_jquery',1);

This will load the WordPress bundled version of jQuery and will make sure that it is always loaded into your head of the site.

EDIT

If you want to enqueue your own or existing jQuery rather than the bundled version then you can modify the hook by passing it a $src parameter.

function royal_insert_jquery(){

    wp_deregister_script('jquery');
    wp_register_script('jquery', get_template_directory_uri().'/javascripts/jquery.js', array(), false, false);
    wp_enqueue_script('jquery');
}

add_filter('wp_enqueue_scripts', 'royal_insert_jquery', 1);

Use the WordPress Codex as a reference so you know what parameters are required and can be passed and how to go about using the hook correctly. Here is the link: wp_enqueue_scripts()