Dana Ross

Dave’s WordPress Live Search adds “live search” functionality to your WordPress site. As visitors type words into your WordPress site’s search box, the plugin continually queries WordPress, looking for search results that match what the user has typed so far.
The <a href="http://ajaxpatterns.org/Live_Search" rel="nofollow ugc">live search</a> technique means that most people will find the results they are looking for before they finish typing their query, and it saves them the step of having to click a submit button to get their search results.
This functionality requires Javascript, but the search box still works normally if Javascript is not available.
http://www.youtube.com/watch?v=7CGR2bJ1mLM 
<a href="https://plugins.svn.wordpress.org/daves-wordpress-live-search/assets/intro_video_transcript.txt" rel="nofollow ugc">transcript</a>
This plugin is compatible with the <a href="https://wordpress.org/extend/plugins/xlanguage/" rel="ugc">xLanguage</a> and <a href="http://wpml.org/" rel="nofollow ugc">WPML</a> plugins for internationalization (i18n) of search results.
<h3>Filters</h3>
See <a href="https://plugins.svn.wordpress.org/daves-wordpress-live-search/trunk/filter_examples.php" rel="nofollow ugc">filter_examples.php</a> in 
the plugin files for examples of how to use these filters. Remember, these filters only affect the 
Dave’s WordPress Live Search display, not the normal WordPress search results or the posts themselves.
<ol>
<li>dwls_alter_results</li>
<li>dwls_attachment_thumbnail</li>
<li>dwls_post_title</li>
<li>dwls_the_excerpt</li>
<li>dwls_post_date</li>
<li>dwls_author_name</li>
<li>dwls_alter_result_template</li>
<li>dwls_post_custom</li>
<li>dwls_query_fields</li>
</ol>
<h3>Wish List</h3>
Features I want to implement in future releases:
<ol>
<li>“No results found” message (optional)</li>
</ol>

Dave's WordPress Live Search

At first, this seems like a good plugin and it is. I tried to report a bug a couple of months ago and, despite the fact the plugin says it's compatible with the latest version of WordPress, there seems to be bugs that are not addressed. At this point, I had to hack the plugin and edit source code to make it work.

Unmaintained plugin

You do a great job

Adds "live search" functionality to your WordPress site. Uses the built-in search and jQuery.

Anil Ankola

A WordPress Better Ajax Live SearchWP plugin created by Anil Ankola for your website live search plugin show instant search results as soon as you type in the keyword without reloading the page.
Features
<ul>
<li>Better Ajax Live SearchWP add menu in dashboard sidepanel</li>
<li>Better Ajax Live SearchWP choose background, title, text, button and separator color options in Better Ajax Live SearchWP menu settings admin</li>
<li>Shortcode System.</li>
<li>Use this shortcode [better_ajax_live_search] show live search.</li>
<li>WordPress Live Search Enabled.</li>
<li>Easy to Use.</li>
<li>You can use it in posts or pages.</li>
</ul>

Better Ajax Live SearchWP

Better Ajax Live SearchWP plugin is a live search plugin for WordPress without reloading the page.

Dave's WordPress Live Search vs Better Ajax Live SearchWP