[JWait]

Are you trying to include your "popular categories" within the "All Categories" box or separately? Do you want "flyout menus" or just a list?

Anyway, the easiest way is to make a "clone" of common_files/customer/categories.tpl naming it popular_categories.tpl.

Something like this...

{capture name=menu}
  {assign var="additional_class" value="menu-fancy-categories-list"
  <ul>
    
      <li{interline name=categories}><a href="LINK TO CATEGORY" title="CATEGORY NAME">CATEGORY NAME</a></li>

  </ul>

  {assign var="additional_class" value="menu-categories-list"}

{/capture}
{include file="customer/menu_dialog.tpl" title="Popular Categories" content=$smarty.capture.menu}
{/if}

Change the part that says "<li{interline name=categories}><a href="LINK TO CATEGORY" title="CATEGORY NAME">CATEGORY NAME</a></li>" to your link and title, and repeat for each category.

Then, in customer/left_bar.tpl for whatever skin you are using, look for
{include file="customer/categories.tpl"}

and just above it add
{include file="customer/popular_categories.tpl"}

EDIT: I made a mistake and forgot to exclude "flyout menus" in my original post (fixed now)