Alisha provides a list of Ajax powered WordPress themes. You may want to try one or more.Some of them are good, Some are limited to one or two features like search. Some not found. But worth a look if you plan to use Ajax in your templates.
This is a WordPress plugin which adds power, usability, and the beauty of AJAX to WordPress based blogs and WordPress based websites. The plugin improves the user experience, the administration capabilities, and the design potential or the blog/site.
So how about writing your own WordPress plugins with Ajax? WordPress codex helps you to begin: http://codex.wordPress.org/AJAX_in_Plugins
Finally, here are four plugins discussed. http://www.linuxjournal.com/article/9574 This should help you get more ideas to start.