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

Code for the People Ltd

Scott (@scottsweb)

WP Ajax Search Widget is a replacement for the standard search widget but instead of redirecting you to a new search page the results are returned underneath the search input with an option to click through to the standard results page.
The widget allows you to choose how many results to show.
<a href="http://scott.ee/" title="WordPress designer and developer" rel="nofollow ugc">a plugin by Scott Evans</a>

WP Ajax Search Widget

Displays instant search results directly beneath a search widget.

Live Search Popup vs WP Ajax Search Widget