ajberasategui

This plugin provides a Search Widget similar to the default WordPress one but with the abilty of adding category select 
lists to restrict the search query to only those categories.
Any comments, reviews, support questions are very much welcome!!!

AB Categories Search Widget

Insert a search form widget that allows visitors to add category filters to the search query.

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.

AB Categories Search Widget vs Faceted Search