I've heard some people propose that it will be 3-dimensional. Apparently some government agencies have created their own Intranets in 3D claiming it makes it easier to find stuff (not sure if I believe this or not...). If it's true, though, then I wouldn't be surprised to see it on the consumer web in the near to medium-term future.
True 3D doesn't make sense for a lot of kinds of data. Images are inherently planar.
My limited hope is that the web can be as peppy as today's desktop interfaces. The elephant in the room of "Web 2.0" is how slow lots of implementations of asynchronous server communication are.
