Image and video manipulation, alternate widget sets (which nowadays tend to require at least one of heavy image manipulation or OpenGL to really work correctly), 3D applications that actually work and aren't just static models rotating (because now you can actually afford to manipulate vertexes with some intelligence). Online games that use a combination of these techniques. Apps that grab video from your webcam and do something with it. (Mozilla demonstrated that: http://arstechnica.com/open-source/news/2009/02/mozilla-demo... ) The dream of doing distributed computing by just visiting a web page could come true (like for X@Home). An OS in your browser would become not-a-joke. Native VNC instead of flash. Native encryption run by the app instead of the browser, possibly permitting ssh-in-the-browser. Actual typesetting could be implemented (surprisingly computationally expensive) allowing actual competition in the Office space.

You rather proved my point, unfortunately. Web apps are not about "DOM manipulation". They are about delivering no-install applications over the internet. They have historically been about DOM manipulation because that was all they could afford to do performantly (and that only barely at times). As that changes, so does the web. We're getting a ways along this path anyhow (http://code.google.com/p/quake2-gwt-port/ ), just with increasingly fast JS and other tech, but it's only going to grow more.