List Categories AND their associated entries
Something along the line of this should do that:

&lt;ul&gt;
    {% for category in craft.categories.group('categoryGroupHandle') %}
    &lt;li&gt;
        {{ category.title }}
        {% for entry in craft.entries.section('sectionHandle').relatedTo(category) %}
            {% if loop.first %}&lt;ul&gt;{% endif %}
                &lt;li&gt;&lt;a href="{{ entry.url }}"&gt;{{ entry.title }}&lt;/a&gt;&lt;/li&gt;
            {% if loop.last %}&lt;/ul&gt;{% endif %}
        {% endfor %}
        &lt;/ul&gt;
    &lt;/li&gt;
    {% endfor %}
&lt;/ul&gt;


Probably some bugs in here, but should be enough to get you started.

Also probably smart to wrap this in {% cache %} tags, as it probably will trigger a lot of database queries.