jano wp and woocommerce advanced search is the best plugin for wordpress and woocommerce, autosuggest products and posts search,
A powerful ajax search engine for WordPress.
The WP Search plugin replaces WordPress search with a better search that is fully customizable via the dashboard, API, filters and action hooks.
Adjust WordPress search results to order by relevance, not by date.
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.