Adam Doppelt investigated a number of open source AJAX spell checkers recently for Jobster. (His home page, by the way, sets some sort of record for understatedness.)

One of the coolest spell checkers he found was Emil Eklund’s DHTML Spell Checker. It implements background spell checking with red squiggly underlines for mispellings and a drop down menu of suggested corrections. It’s licensed under the MIT license so you should have no issues using it on your own site.

This post and this one describe in more detail how it works.