TCBarrett

This plugin requires is just the front end javascript library, the following two things to be done in support: 
1. Add the class ‘simpleajaxform’ to your form. 
2. Make sure you have the correct wp_ajax handler hook defined.
It was primarily built as an example for a blog post.

Simple AJAX Form

A simple jQuery javascript library to ajax enable forms.

Konstantin Obenland

This plugin uses an abstraction of jQueryUI’s autocomplete widget that interacts with the unofficial/undocumented Google Suggest API. 
Props go to Haochi Chen.
It adds an AJAX call to the search form, returning matches for the current search query. 
Make sure the searchform input field has <code>id="s"</code> applied, so this plugin can hook in the existing WordPress API to unfold its magic.
<h4>Translations</h4>
I will be more than happy to update the plugin with new locales, as soon as I receive them! 
Currently available in:
<ul>
<li>English</li>
<li>Serbian</li>
</ul>

WP Google Suggest

sir,
plugin not work why  ?
I need the plugin working in my site . But it does not work correctly .
Help me !!!!!!!
Regards
Mostafijur



plugin not work why

Provides suggestions while typing a search query, using the Google Suggest API.

Simple AJAX Form vs WP Google Suggest