Applets and other embedded objects (e.g Flash, Silverlight) for a 'public' website? No way, even eBay and Amazon avoid them. Personally, I tend to despise the type of stupid eye candy this crap presents and avoid sites that try to hide a poorly designed interface behing this curtain of crap. If you feel otherwise, stop asking, there's nothing anyone can do for you.
As a way to deploy a very rich and capable GUI application to a pre-defined set of end users, applets will cause more problems than they cure because they need to operate within the 'sandbox' of a web browser. Security and development issues will be a problem, along with what that damn back button causes.
Sun overcame this problem with Java WebStart (Microsoft ClickOnce followed soon thereafter), allowing applications to be installed and updated as required from a central web server. Works incredibly well from my admittedly narrow perspective.