Ufortunately, not in the near future. At best they will only really go along the lines of Flash/Java Applets/Siverlight, and just be (mostly) black boxes embedded in html.
Not that I have anything against html per se, I make most of my living doing web sites and related programming, having wrangled with html (+css + js +asp/php/cgi/aspnet/jsp...) since netscape was big, along with the associated browser compatibility issues.
Web developers have been fighting tooth and nail with the limitations of html for years now, and the ever increasing expectations of clients of a more desktop like experience doesn't make it any easier.
Sure we have some fancier tachniques like ajax to play with, and browsers' js engines are getting better, but html still shows the limitations of its roots as relatively static publishing medium. But it is the dominant medium, and wont go away any time soon.
HTML 5 promises to make some improvements, but has been at the centre of a nerd war for way too long, at least a few years before we see any significant changes there.