WordPress/WooCommerce Search makes your user's search for products/posts/formus/topics quick and useful. This could be achieved using a simple Short code.
For detailed steps with screenshots including how to register your site on Google Custom search please visit http://phpwpinfo.com/replace-wordpress-search-with-google-custom-search-cse/
Fueto is a free, fully-hosted, API-based, outsourced search engine for your WP blog. Fueto wins because we use social signals to rank search results.
Live search suggestions for all post types. Search everywhere, include almost everything in the search. WooCommerce compatible.
Other features
This plugin converts default WordPress search to full screen search overlay form on your WordPress website.
This plugin removes the need to visit All Posts, All Pages, All Users, All Products & All Orders to do a search. Fewer clicks to get things done.
This plugin is no longer in development - A search engine for WordPress that indexes ALL of your site and provides comprehensive search.
WordPress Live Ajax Search
The WP Search plugin replaces WordPress search with a better search that is fully customizable via the dashboard, API, filters and action hooks.
Create a Full Screen Search Overlay Effect in WordPress.
Search Manager Lite allows you to enhance WordPress and WooCommerce search with the ability to search by extra fields like comments, excerpt, SKU etc.
The plugin adds an advanced search form with search suggestions using a shortcode.
Hide any post or page from the search results.