Ajax SuggestBox
The free Ajax SuggestBox will render a search input box that drops down with suggestions as-you-type on a web page. The Javascript and server-side script for getting suggestions available for download.
The most useful applications of this type of suggest I’ve seen are for entering freeform tags in del.icio.us, and for a Wikipedia search at WikiWax. Of course, there’s always Google Suggest which I think started the whole suggest theme. Any others out there?