nchankov

This plugin adding autocomplete functionality to search input field. It is using core jQuery library as well as 
autocomplete jquery plugin from http://www.pengoworks.com/workshop/jquery/autocomplete.htm
This plugin requires zero configuration, but since version 1.2.0 there is admin screen where you can enable the extra ‘number of matches’ next to each option and other goodies. 
You just need to activate and it’s ready to be used in the blog. The plugin is tested with WordPress 2.6.5, but until there aren’t big core changes, it sould work for all future releases. I don’t have 
information if this plugin will work with older versions of WordPress, but for sure it is working with 2.6.x. The last version 1.2.0 is tested on WP 2.7.1.
New in 1.3.5: When it’s selected to display posts and/or pages and the autosubmit is ON, then when the user clicks on the selected row it will go directly to the post or page url. This way user are skipping one step. The change affect only pages and posts. Categories and tags behave as now.
New in 1.3.0: Added result type option in admin. From now on you can choose which type of results will be displayed.
New in 1.2: This version could display number of matches found in the blog.
New in 1.2.1: Small fix for table prefixes and adding autosubmit once the item from the list is selected.
I would appreciate if you write an review/post in your blog with a link to my page: <a href="http://nik.chankov.net" rel="nofollow ugc">nik.chankov.net</a>. 
Thanks!
<h3>Thanks to</h3>
<ul>
<li><a href="http://nik.chankov.net" rel="nofollow ugc">My Self 🙂</a></li>
<li><a href="http://jquery.com" rel="nofollow ugc">jquery.com</a></li>
<li><a href="http://www.pengoworks.com/workshop/jquery/autocomplete.htm" rel="nofollow ugc">jQuery Autocomplete Plugin</a></li>
<li><a href="http://csixty4.com/" rel="nofollow ugc">Dave Ross</a> for the hint with name selector 🙂</li>
</ul>

Autocompleter

Adding autocomplete functionality to the blog search input field. The values provided are the tags and categories used in the blog.

jojaba

This plugin is meant to add the word autocomplete in search input field by using the index stored in Relevanssi database. So you have to <a href="https://wordpress.org/plugins/relevanssi/" rel="ugc">install first Relevanssi</a> (free or premium version) to have it to work.
The JS script used to accomplish the autocompletion work has been developed by <a href="http://lea.verou.me/" rel="nofollow ugc">Lea Verou</a> and is called <a href="https://leaverou.github.io/awesomplete" title="Go to the Awesomplete homepage" rel="nofollow ugc">Awesomplete</a>. It is very simple to set up, lightweight and accessible.
<h4>List of functionalities</h4>
<ul>
<li>Settings available: styling, min characters typed to show the autocompletion box, max suggestions in autocompletion box.</li>
<li>Get the Relevanssi Indexed words to have the autcompletion list</li>
<li>Fast and lightweight</li>
<li>English and french languages included</li>
</ul>

Autocomplete For Relevanssi

Relevanssi author here. Please do not use this plugin in its current form. It's dangerous for performance and may cause server crashes. It will also slow down page loads in a rather terrifying manner.

Dangerous, do not use

Autocompletion functionality for WordPress search input when Relevanssi plugin is installed.

Autocompleter vs Autocomplete For Relevanssi