One really short, simple answer... you can't :D
Flash requires an embed tag, an image requires an embed tag etc, so you'd have to use HTML in some method or another.
PHP is an embedded language, it is used to generate HTML on which the browsers renders, with XML, well technically a browser like Ie or FireFox will render it in it's own way for readability, but I would not class that as a website.
The major developments in the world of web technologies involves the development of HTML and CSS to improve them, there isn't any need for an alternative. In fact we're pushing towards a standard, what point would there be in introducing a new language to negate these standards. The whole IE saga would simply get worse.
Like the others have suggested, you could directly load an image or a flash file, but an image is useless on it's own, and a flash interface throws up loads of problems like SEO, accessibility etc, not least it's very heavy and usually completely misused. In my mind I wouldn't even class this method as a website, it just doesn't tick any of the boxes (IMO).