AndrewUlrich

<p>This plugin creates two widgets:</p>
<ol>
<li>A widget where you can choose from all the categories in your blog.</li>
</ol>
<p>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.</p>
<ol>
<li>A widget where you can choose from all the tags in your blog</li>
</ol>
<p>You can select the tags you want to search for, and it will only show posts that have all of the tags you selected.</p>
<h3>Known Issues</h3>
<p>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.</p>
<p>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.</p>


Faceted Search

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

Freemius

vegacorp

Jose Vega

<p><strong>This plugin works with Gutenberg (new editor). It works with the classic editor and the gutenberg editor.</strong></p>
<p>Require users to select a taxonomy term when publishing posts. For example, require the selection of a category or tag.</p>
<h4>It works with</h4>
<ul>
<li>All taxonomies , including post categories , post tags , product categories, product tags, and custom taxonomies.</li>
<li>All post types , including posts, pages, WooCommerce Products, Events, etc.</li>
</ul>
<h4>Use cases</h4>
<ul>
<li>Force users to select a category when publishing posts</li>
<li>Force users to select a tag when publishing posts</li>
<li>Force users to select a custom taxonomy term when publishing posts</li>
<li>Force users to select a category when publishing WooCommerce Products</li>
<li>Force users to select a tag when publishing WooCommerce Products</li>
<li>Force users to select a category or tag when publishing Events</li>
<li>Force users to select any Taxonomy Term when publishing any custom post type</li>
</ul>
<p>This plugin is completely free.</p>


WP Required Taxonomies – Categories and Tags Mandatory

Great for making categories required , so users can´t publish without selecting a category.

Great

Force users to select a taxonomy term when publishing posts. For example, make category or tags required

Faceted Search vs WP Required Taxonomies – Categories and Tags Mandatory