Take the browser window and slap it in a canvas. By default it could look like Firefox/Safari etc, but unlike them you can zoom out to find a graph showing your history. If I started out at page A and then click on B and then opened a new tab AA when I zoomed out to the graph view I would see the following:
Scrolling up and down there could be lines highlighting the hour/day change making it easy to find where you were. All pages that you visit in your history will be indexed and be searchable. Typing in searching will hide nodes that don't apply leaving the remaining ones that are left easy to browse around.
Because the browser is built on top of the canvas animations and transitions will be very easy to implement. Features that you have seen on the iPhone and in the newer 3d window managers can be done with ease. Going back could have the page scroll off the bottom of the screen and the previous site scroll down and subtly "bounce" into the window.
Developers could add all sorts of features, hit and key and like OS X's dashboard you can flip around a webpage and dissect it, information nodes/boxes could pop off all sides and with zooming in and out of the canvas there is plenty of room for all sorts of addons and details about the site without having to sacrifice because of space.
Or when a webpage is flipped over there would be all the user addons such as the ability to list what filters apply to that site, if cookies should be allowed, etc
Update: Check out what Zack has done with wekit on a canvas.