From http://ecommerce.shopify.com/c/ecommerce-design/t/multi-level-menus-in-shopify-is-there-a-definitive-answer-138415

new_gist_file

<nav role="navigation">
  <ul>
    {% for link in linklists.main-menu.links %}
    {% assign child_list_handle = link.title | handle %}
    {% if linklists[child_list_handle] and linklists[child_list_handle].links.size > 0 %}
    <li class="has-dropdown">
      {{ link.title | link_to: link.url }}
      <ul>
        {% for child_link in linklists[child_list_handle].links %}
        {% assign grand_child_list_handle = child_link.title | handle %}
        {% if linklists[grand_child_list_handle] and linklists[grand_child_list_handle].links.size > 0 %}
        <li class="has-dropdown">
          {{ child_link.title | link_to: child_link.url }}
          <ul>
            {% for grand_child_link in linklists[grand_child_list_handle].links %}
            <li>
              {{ grand_child_link.title | link_to: grand_child_link.url }}
            </li>
            {% endfor %}
          </ul>
        </li>
        {% else %}
        <li>
          {{ child_link.title | link_to: child_link.url }}
        </li>
        {% endif %}
        {% endfor %}        
      </ul>
    </li>
    {% else %}
    <li>
      {{ link.title | link_to: link.url }}
    </li>
    {% endif %}
    {% endfor %}
  </ul>
</nav>