asimeon

Costumizable search widget. Shows the search results dynamic on your sidebar.
Features:
<ul>
<li>Show or don’t show a searchfield or configure another input field</li>
<li>Configure the search: post type, categories, tags, post title and content</li>
</ul>

Dynamic Search Widget

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.

Dynamic Search Widget vs AB Categories Search Widget