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.

Alkaweb

Add to your site a top-notch live search field.
Eonet Live Search can be added to any search field. 
It’ll create a nice popup box with the search’s result in real time. It plays very well with Buddypress, Woocommerce 
and any other custom post type. Specific integration can be added by us.
<a href="http://alka-web.com/eonet/live-search/" rel="nofollow ugc">Live Demo</a>
<h4>Featured features:</h4>
<ul>
<li>Options panel</li>
<li>Buddypress Members integration</li>
<li>Buddypress Groups integration</li>
<li>Buddypress Activities integration</li>
<li>Works with any custom post types</li>
<li>Pages / Posts integration</li>
<li>AJAX powered, no page reload</li>
<li>User search history</li>
<li>Options to restrain the search sections</li>
<li>Results listed within organized tabs</li>
</ul>
<h4>For developers:</h4>
<ul>
<li>Hooks/Filters available in all the plugin code</li>
<li>Minified files</li>
<li>Documented code</li>
<li>GPL license</li>
<li>Secure development using tokens and WordPress native functions</li>
</ul>
If you’re looking for a next generation live search plugin, you should give it a go!
We’re open to any feature suggestion.
This plugin has been developed as a side project by the Alkaweb developers team.

Eonet Live Search

It's an useful and pretty flexible plugin!

I like it

Search dynamically in real time through all your site, including pages, posts, members, products & so on.

Dave's WordPress Live Search vs Eonet Live Search