Example code:

{exp:dyno_cat:categories weblog="weblog1" show_empty="no" status="open" default_parent_only="yes"}

{if c_current_category}<b>{/if}<a href="{path=weblog/test}">{category_name}</a> {category_count}
{if c_current_category}</b>{/if}

{/exp:dyno_cat:categories}

All the parameters and variables available in the {exp:weblog:categories} are available, as well as a few additions.
Added parameters:

-default_parent_only - “yes” or “no” (default)
In order for anything ‘dynamic’ to happen, the parents_only parameter MUST be off (that’s what it defaults to anyway). However, I wanted my NON-category pages to show parents only. This parameter determines whether subcats are shown on NON-category pages.

-status - accepts pipe deliniated lists of article status, used with the {count} variable AND in conjunction with the show_empty parameter. Default is “all” statuses.

-group_id - if you manually specify the group id, it saves a query. Otherwise it looks it up for you. Note- only a SINGLE group_id can be used.

-weblog_id - if you want to restrict display so that empty categories aren’t displayed AND more than one weblog uses the same category group, you can specify a specific weblog or weblogs ("1|3|4").

-active_id - still experimental, it currently takes one parameter- active_id="current". If this parameter is set, then when on a category page, the li will be given a css id="active".

-single_tree - still experimental, it currently takes one parameter- single_tree="all". If this parameter is set, then when on a category page ONLY the categories in that heirarchy will show (the other parent cats won’t).

-disable - if you aren’t using the {count} variable, you should include disable="count" and save yourself a query.

**Note- as with all EE tags, the cache="yes" refresh="60" parameters work with this tag, which is handy.

Added variables:
{category_count}
{parent_id}

Configuration options:
If you open up this file in an editor, you can set three user defined variables at the top of the file:

var $before_number = '(';
var $after_number = '(';
var $zero_count = '';

These just specify enclosing code for the category count number (kinda useless) and $zero_count determines what is displayed for the {category_count} if the count is 0.