nodstrum.com has posted a jQuery auto-complete tutorial which integrates with PHP/MySQL.
There are literally tons of Ajax resources out there, perhaps too many to digest in one sitting, and one can get overwhelmed with the right framework to use and in what context to use them, but I do find AjaxRain to be a good resource for finding upcoming and current Ajax apps.
Links;
- jQuery auto-complete tutorial with PHP/MySQL (nodstrum.com)
- AjaxRain