AndrewUlrich

This plugin creates two widgets:
<ol>
<li>A widget where you can choose from all the categories in your blog.</li>
</ol>
This is similar to what newegg.com uses, where you can select multiple categories, and it will only show posts belonging to all the categories you select, and such categories can be narrowed down by selecting their subcategories.
<ol>
<li>A widget where you can choose from all the tags in your blog</li>
</ol>
You can select the tags you want to search for, and it will only show posts that have all of the tags you selected.
<h3>Known Issues</h3>
After upgrading from 2.1 to 2.2 it is highly recommended that you deactivate the plugin and then re-activate it. Unfortunately WordPress 3.1 no longer calls register_activation_hook when the plugins are upgraded, so this may be necessary, otherwise you may not see all your categories.
When using version 3.2 or above, and excluding categories, the display order may or may not be mixed up when you exclude a parent category.

Faceted Search

This plugin will create widgets that you can use to conduct faceted searches using the categories or tags on your site.

Matthew Muro

Multi-Column Taxonomy List is a plugin that allows you to list your categories, tags, or custom taxonomies into multiple columns.
This plugin is great to use on custom archives index pages to display all categories, tags, and custom taxonomies on a single page. You can also turn the list into links to the RSS feeds for your taxonomies.
<h3>Usage</h3>
<h4>Shortcode attributes</h4>
You can implement a new list by adding the shortcode <code>[mctl]</code> to the content of a page. By default, it will output the categories into three columns with a heading of Categories. You can customize the output using attributes in the following format: <code>[mctl taxonomy='post_tag' title='Tags']</code>
<ul>
<li>taxonomy: The taxonomy to retrieve terms from
<ul>
<li>Valid values: <code>category</code>, <code>post_tag</code>, <code>custom_taxonomy_name</code></li>
<li>Multiple values not allowed</li>
<li>Default: <code>category</code></li>
</ul>
</li>
<li>title: Sets the title of the list
<ul>
<li>Valid values: any string</li>
<li>Default: <code>Categories</code></li>
</ul>
</li>
<li>title_container: HTML element to wrap the title in
<ul>
<li>Valid values: any HTML element</li>
<li>Recommended values: <code>h1</code>, <code>h2</code>, <code>h3</code>, <code>h4</code>, <code>h5</code>, <code>h6</code>, <code>p</code></li>
<li>Default: <code>h3</code></li>
</ul>
</li>
<li>columns: Sets the number of columns to use
<ul>
<li>Valid values: any integer</li>
<li>Default: <code>3</code></li>
</ul>
</li>
<li>orderby: Sort terms by name, unique ID, slug, or the count of posts in that term
<ul>
<li>Valid values: <code>name</code>, <code>id</code>, <code>slug</code>, <code>count</code></li>
<li>Default: <code>name</code></li>
</ul>
</li>
<li>order: Sort order for the terms (either ascending or descending)
<ul>
<li>Valid values: <code>ASC</code>, <code>DESC</code></li>
<li>Default: <code>ASC</code></li>
</ul>
</li>
<li>alpha_grouping: Output the first letter of each alphabetical grouping
<ul>
<li>Valid values: <code>0</code>, <code>1</code></li>
<li>Default: <code>0</code></li>
</ul>
</li>
<li>show_count: Toggles the display of the current count of posts in each term. <code>0</code> is false/off and <code>1</code> is true/on
<ul>
<li>Valid values: <code>0</code>, <code>1</code></li>
<li>Default: <code>0</code></li>
</ul>
</li>
<li>exclude: Exclude one or more terms from the results.
<ul>
<li>Valid values: unique IDs, separated by commas. (ex: <code>exclude='12,13,22'</code>)</li>
<li>Default: no default</li>
</ul>
</li>
<li>parent: Get direct children of this term
<ul>
<li>Valid values: any integer</li>
<li>Multiple values not allowed</li>
<li>Default: no default</li>
</ul>
</li>
<li>child_of: Get all descendents of this term
<ul>
<li>Valid values: any integer</li>
<li>Multiple values not allowed</li>
<li>Default: <code>0</code></li>
</ul>
</li>
<li>rss: Turns the list into links to RSS feed of term. <code>0</code> is false/off and <code>1</code> is true/on
<ul>
<li>Valid values: <code>0</code>, <code>1</code></li>
<li>Default: <code>0</code></li>
</ul>
</li>
<li>rss_image: Use a custom image RSS image icon when <code>rss</code> is on.
<ul>
<li>Valid values: full URL to image</li>
<li>Default: <code>/wp-includes/images/rss.png</code></li>
</ul>
</li>
<li>number: Max number of terms to display
<ul>
<li>Valid values: any integer</li>
<li>Default: display all terms</li>
</ul>
</li>
<li>like: Return terms that begin with this value
<ul>
<li>Valid values: any string</li>
<li>Default: no default</li>
</ul>
</li>
<li>search: Return terms that contain the ‘search’ string
<ul>
<li>Valid values: any string</li>
<li>Default: no default</li>
</ul>
</li>
</ul>
<h4>Template tag</h4>
Alternatively, you can implement a new list by adding the the template tag <code><?php multi_column_tax_list(); ?></code> anywhere in the code of your theme. Just like the shortcode, by default it will output the categories into three columns with a heading of Categories. You can customize the output using a string of parameters in the following format: <code><?php multi_column_tax_list( 'taxonomy=post_tag&title=Tags' ); ?></code>
Refer to the above attributes for customizations.

Multi-Column Taxonomy List

List your categories, tags, or custom taxonomies into multiple, customizable, columns.

Faceted Search vs Multi-Column Taxonomy List