After Justin had been playing with these types, we check out the possibilities of types for "Movies".

Simple Solution

function post_type_movies() {
	register_post_type( 'movies',
                array( 'label' => __('Movies'), 'public' => true, 'show_ui' => true ) );
	register_taxonomy_for_object_type('post_tag', 'movies');
}
add_action('init', 'post_type_movies');

More parameters for meta-boxes

Of course there are a number of parameters for this function and so the behavior and appearance of the corresponding edit page can be controlled quite easily, a small sample with additional meta boxes:

function post_type_movies() {
	register_post_type(
                     'movies',
                     array('label' => __('Movies'),
                             'public' => true,
                             'show_ui' => true,
                             'supports' => array(
                                        'post-thumbnails',
                                        'excerpts',
                                        'trackbacks',
                                        'custom-fields',
                                        'comments',
                                        'revisions')
                                )
                      );
	register_taxonomy_for_object_type('post_tag', 'movies');
}
add_action('init', 'post_type_movies');

The default arguments

// Args prefixed with an underscore are reserved for internal use.
$defaults = array(
    'label' => false,
    'publicly_queryable' => null,
    'exclude_from_search' => null,
    '_builtin' => false,
    '_edit_link' => 'post.php?post=%d',
    'capability_type' => 'post',
    'hierarchical' => false,
    'public' => false,
    'rewrite' => true,
    'query_var' => true,
    'supports' => array(),
    'register_meta_box_cb' => null,
    'taxonomies' => array(),
    'show_ui' => null
);

• label - A descriptive name for the post type marked for translation. Defaults to $post_type
• public - Whether posts of this type should be shown in the admin UI. Defaults to false
• exclude_from_search - Whether to exclude posts with this post type from search results. Defaults to true if the type is not public, false if the type is public
• publicly_queryable - Whether post_type queries can be performed from the front page. Defaults to whatever public is set as
• show_ui - Whether to generate a default UI for managing this post type. Defaults to true if the type is public, false if the type is not public
• inherit_type - The post type from which to inherit the edit link and capability type. Defaults to none
• capability_type - The post type to use for checking read, edit, and delete capabilities. Defaults to "post"
• edit_cap - The capability that controls editing a particular object of this post type. Defaults to "edit_$capability_type" (edit_post)
• edit_type_cap - The capability that controls editing objects of this post type as a class. Defaults to "edit_ . $capability_type . s" (edit_posts)
• edit_others_cap - The capability that controls editing objects of this post type that are owned by other users. Defaults to "edit_others_ . $capability_type . s" (edit_others_posts)
• edit_others_cap - The capability that controls publishing objects of this post type. Defaults to "publish_ . $capability_type . s" (publish_posts)
• read_cap - The capability that controls reading a particular object of this post type. Defaults to "read_$capability_type" (read_post)
• delete_cap - The capability that controls deleting a particular object of this post type. Defaults to "delete_$capability_type" (delete_post)
• hierarchical - Whether the post type is hierarchical. Defaults to false
• supports - An alias for calling add_post_type_support() directly. See add_post_type_support() for Documentation. Defaults to none
• register_meta_box_cb - Provide a callback function that will be called when setting up the meta boxes for the edit form. Do remove_meta_box() and add_meta_box() calls in the callback
• taxonomies - An array of taxonomy identifiers that will be registered for the post type. Default is no taxonomies. Taxonomies can be registered later with register_taxonomy() or register_taxonomy_for_object_type()

Including Custom Taxonomies

In the following example we include in our Post-Type a Taxonomy with two possibilities; own Tags and categories for Post-Type Movies, the classical tag, without hierarchy and one as category, tag with hierarchies.

function post_type_movies() {
	register_post_type(
                'movies',
                array(
                        'label' => __('Movies'),
                        'public' => true,
                        'show_ui' => true,
                        'supports' => array(
                                     'post-thumbnails',
                                     'excerpts',
                                     'trackbacks',
                                     'custom-fields',
                                     'comments',
                                     'revisions')
                )
        );

	register_taxonomy( 'actor', 'movies', array( 'hierarchical' => true, 'label' => __('Actor') ) ); 

        register_taxonomy( 'production', 'movies',
		array(
                         'hierarchical' => false,
			 'label' => __('Production'),
			 'query_var' => 'production',
			 'rewrite' => array('slug' => 'production' )
		)
	);
}
add_action('init', 'post_type_movies');

Definitely a very interesting and useful feature which provides many possibilities to play around with.

Following solution only works with WordPress 2.5 or higher. If you need help for a lower version, let me know in the comment field and I'll try to help.

Number of posts

$num_posts = wp_count_posts( 'post' );
$num_posts = $num_posts->publish; //publish, draft

Number of pages

$num_pages = wp_count_posts( 'page' );
$num_pages = $num_pages->publish; //publish

Number of categories

$num_cats  = wp_count_terms('category');

Number of Tags

$num_tags  = wp_count_terms('post_tag');

Number of comments

$num_comm  = get_comment_count();
$num_comm  = $num_comm['approved']; //approved, awaiting_moderation, spam, tot

// Solution 2
$num_comm2 = wp_count_comments( );
$num_comm2 = $num_comm2->approved; //approved, moderated, spam, total_comments

Output

The above syntax shows simple how to get the values without including HTML. In another example I show you all results in HTML as a list. Everybody can adjust the format to integrate in their design.

<?php
$num_posts = wp_count_posts( 'post' );
$num_posts = $num_posts->publish; //publish, draft
$num_posts = sprintf( __ngettext( '%s Post', '%s Posts', $num_posts ), number_format_i18n( $num_posts ) );

$num_pages = wp_count_posts( 'page' );
$num_pages = $num_pages->publish; //publish
$num_pages = sprintf( __ngettext( '%s Page', '%s Pages', $num_pages ), number_format_i18n( $num_pages ) );

$num_cats  = wp_count_terms('category');
$num_tags  = wp_count_terms('post_tag');

$num_comm  = get_comment_count();
$num_comm  = $num_comm['approved']; //approved, awaiting_moderation, spam, total_comments
$num_comm  = sprintf( __ngettext( '%s Categorie', '%s Categories', $num_comm ), number_format_i18n( $num_comm ) );
$num_comm2 = wp_count_comments( );
$num_comm2 = $num_comm2->approved; //approved, moderated, spam, total_comments

echo '<ul>';
echo '<li>Posts: ' . $num_posts . '</li>';
echo '<li>Pages: ' . $num_pages . '</li>';
echo '<li>Categories: ' . $num_cats . '</li>';
echo '<li>Tags: ' . $num_tags . '</li>';
echo '<li>Comments: ' . $num_comm . '</li>';
echo '<li>Comments 2: ' . $num_comm2 . '</li>';
echo '</ul>';
?>

You can adjust the design of these lists. You can use classes or IDs. An example is in article „Total Amount of Comments“ (in german language), where you can see a button with the amount of comments.