Site Search 360 - Site Search 360 enhances and improves your built-in CMS or product search with autocompletion, semantic search, filters, facets, detailed analytics, and a whole lot of customization options.
WebshopLogic WP Google Search - Free plugin for integrating Google Custom Search box into your WordPress website without coding.
Relevanssi - Relevanssi replaces the standard WordPress search with a better search engine, with lots of features and configurable options.
WebberZone Better Search - Better Search is a WordPress plugin that automatically replaces the default WordPress search with an enhanced contextual based search engine
Ivory Search - Ivory Search is a WordPress search plugin that improves WordPress Search by providing advanced options to extend search or exclude specific content from search.
Ajax Search Lite - WordPress Live Search plugin - Ajax search lite. A responsive live search engine for WordPress, for free.