You could use AJAX in a generic sense, but you probably do not want to use the AJAX Toolkit (to access salesforce.com features) because the toolkit has to have a valid session ID, and also because AJAX would violate cross-domain security... so you'd have to risk exposing a valid session ID to anyone on the web, and you'd have to use an AJAX proxy (on your server's host) to actually tunnel the connection.
You could use AJAX in a generic sense, but you probably do not want to use the AJAX Toolkit (to access salesforce.com features) because the toolkit has to have a valid session ID, and also because AJAX would violate cross-domain security... so you'd have to risk exposing a valid session ID to anyone on the web, and you'd have to use an AJAX proxy (on your server's host) to actually tunnel the connection.