A starting point, adding the default category to the attachment post type:
add_action( 'init', 'wpse_77550_media_categories' );
function wpse_77550_media_categories()
{
register_taxonomy_for_object_type( 'category', 'attachment' );
}
Or adding a custom taxonomy to the attachment post type (not sure why the taxonomy doesn't show up in the Media menu -show_ui=>true-, although the meta box shows up when editing an attachment):
add_action( 'admin_init', 'wpse_77550_media_taxonomy' );
function wpse_77550_media_taxonomy()
{
$labels = array(
'name' => _x( 'Genres', 'taxonomy general name' ),
'singular_name' => _x( 'Genre', 'taxonomy singular name' ),
'search_items' => __( 'Search Genres' ),
'all_items' => __( 'All Genres' ),
'parent_item' => __( 'Parent Genre' ),
'parent_item_colon' => __( 'Parent Genre:' ),
'edit_item' => __( 'Edit Genre' ),
'update_item' => __( 'Update Genre' ),
'add_new_item' => __( 'Add New Genre' ),
'new_item_name' => __( 'New Genre Name' ),
'menu_name' => __( 'Genre' ),
);
register_taxonomy('genre','attachment', array(
'hierarchical' => true,
'labels' => $labels,
'show_ui' => true,
'show_admin_column' => true,
'query_var' => true,
'rewrite' => array( 'slug' => 'genre' ),
));
}
Reference:
How To: Add Taxonomies to Your Custom Post Types in WordPress