This is feature that your future browser should have. You are probably very well aware that web site addresses (aka as URL) are not user friendly. Using URLs is exactly like asking people to learn MS-DOS commands to handle files.
Most people are not aware of even single URL. In reality people are only aware of brand names, so if www. + brand name + .com works everything is fine, if it doesn't then there is trouble. And if one is after some specific page, which might be: https://bugzilla.mozilla.org/enter_bug.cgi?product=Firefox, situation is more or less helpless.
So let's switch to my father. He navigates the Internet by typing in what he wants to find in search box of a browser, and then he selects page he wants to go to from search results. It is very intuitive, almost always works, and everyone can learn within seconds. Still there is a problem with this type of navigation in today's browsers - this is thought to be only second way of navigating, which means it is far from productive, and fairly unsupported.
So, let's ditch both address and search bar from your browser and keep just one box that handles both thing: Access bar. It should act like following:
- Drop down of address bar should show on its top several pages that are visited, whose title (or better whole content) matches phrase in access bar, and they should be ordered by frequency of visit, it should be possible to expand list if necessary;
- Next section should be devoted to top search engine results, which should be also expandable (and there should be general option to show both title and text description);
- Finally, there should be several search engines listed, to do full search with keywords in Access bar (and this part should be also expandable);
- It should be easy to recognize if someone types in URL, as every single word processor does this, and in this case browser should go to exactly that address.
One should also note that browser must provide solution to mix search results with sponsored search in search results section, as it is highly unlikely that this would be implemented otherwise, as it would have negative commercial effects.