This module provides a backend-agnostic way of showing search suggestions as you type into a search field. This works for both autocomplete suggestions (suggesting search terms to complete what you're typing) as well as live results (showing results that match the search terms you've typed).
It has several components that work together to allow a high level of flexibility and customization. It has a snappy AJAX admin UI, and you can define your own plugins and other classes for use in the module easily.