I think you have to pretty much run with cookies enabled in just about any app except if you're not dealing with anonymous users and you're using Windows Authentication. In all other cases cookies are pretty much required. Especially with AJAX these days old approaches like License Plating are no longer really an option to track a user effectively.
However, it's HIGHLY recommended that you limit your cookie usage to one application level cookie that is some sort of ID that points at server side data to identify users. Typically this is a user id backed by some sort of data store that holds user's session/conifguration information. I would even go as far as recommending not to use Session state it can be really resource intentisve and forces a secondary cookie to track the session.
I think cookies are pretty much accepted these days as long as they are first party cookies and there's only one cookie. With ASP.NET and FormsAuthentication you can use your authentication as the user tracking mechanism with even the ability to store some often reused data directly in the form's authentication ticket itself. Howevr, that does require that users are logged in so you may still need a secondary cookie if you need to track anonymous users.
+++ Rick ---
>I would like to obtain your feedback as to know if you are still using cookies when developing a Web site to keep the authentication? Either as http or https, I would like to know if you prefer to pass the authentication in a query string, by some kind of encrypted (or not) session ID, at every hit instead.