Scott (@scottsweb)

Add Google style instant search and search suggest to your WordPress powered site. This plugin will begin displaying search results as soon as your site visitor starts typing into the search box.
The plugin requires very little configuration and should work out of the box with most themes. The plugin has its own options page to configure the plugin to work with your theme if you require it.
<a href="http://scott.ee/" title="WordPress designer and developer" rel="nofollow ugc">a plugin by Scott Evans</a>

Instant Search & Suggest

Instant WordPress search with search suggestions for tags, categories and titles.

Code for the People Ltd

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.

Instant Search & Suggest vs WP Ajax Search Widget