This plugin adds Spotlight ™ like live search with an ajax popup to 
the default search box. See the screenshot.
It can be used as a widget or directly as a PHP call in the theme.
The Live Search Plugin is heavily based on John Nunemaker’s 
<a href="http://www.wp-plugins-db.org/plugin/addicted-to-live-search/" rel="nofollow ugc">Addicted To Live Search</a>.
<h4>Changelog</h4>
<ul>
<li>1.4.7 Fix by Tony for “With mouseover on result in IE, there is no background image or color”.</li>
<li>1.4.6 Added livesearchpopup_resultsbox(width) to put the popup below a search box of your choice, e.g. from a theme.</li>
<li>1.4.5 Do not initialize if no livesearchpopup_results is found. In contrast to the original live search this plugin does not make sense without the popup anyway. This fixes a JavaScript bug in IE7.</li>
<li>1.4.4 Use wpurl instead of siteurl to allow installations of WordPress at different addresses (thanks to Draco)</li>
<li>1.4.3 Use <?php instead of <? in live-search-popup.php</li>
<li>1.4.2 Force update script to update the plugin.</li>
<li>1.4.1 Switched to the_post instead of the deprecated wp_start().</li>
<li>1.4 Finally permalinks work together with this plugin. In addition a “Show all” links was added at the bottom for the case that there are more posts than shown in the popup (thanks to Marco Luthe).</li>
<li>1.3.4 Moved the placeholder and autocomplete attributes of the search box to JavaScript as they are not XHTML valid (thanks to Marco Luthe)</li>
<li>1.3.3 Added some print commands in front of get_bloginfos (thanks to upekshapriya who noticed that)</li>
<li>1.3.2 Force update script to update the plugin.</li>
<li>1.3.1 Relative paths in css to allow installation which are not at the domain root.</li>
<li>1.3 Fixed behaviour for change and blur events of the search box. This fixes the “click-through” bug.</li>
<li>1.2.1 Updated to reflect that it works with 2.3 as well.</li>
<li>1.2 Bugfixes</li>
<li>1.1 Bugfixes</li>
<li>1.0 First release</li>
</ul>

Live Search Popup

Spotlight (tm) like live search with an ajax popup

wokamoto

You can choose (child) categories and see the posts belong to the chosen category with AJAX.
When the category you choose from the list box has child categories, the child categories will be shown in a new list box. 
Clicking the “Search” button, the list of posts belong to the bottom category which you choose will be displayed under the “Search” button.

Simple Category Search

You can choose (child) categories and see the posts belong to the chosen category with AJAX.

Live Search Popup vs Simple Category Search