Natural Languange Navigation, finally
I have touched this topic at Access bar. After some rethinking, this is how it looks at this point:
This means that user should not type in URLs any more, and that natural language is used for navigation. Of course, user can type in URLs, as browser can easily recognize them and follow them, but this is just a backup solution, and it shouldn't be primary way of navigation. As user types in, he gets Google suggestion (and form history) in the tooltip. Pressing the left key moves pointer to tooltip, and it is very easy to select whole the phrase.
On the other hand, drop down has three parts - History of visited pages, Google search and Google sponsored searched (I am talking about Google here as Firefox default engine, probably it could be other search engine too). Every column contains list with page titles and domain URL. Though I would prefer total removal of domain URL, at this point it is still useful to ensure that there is no fishing. History column is replacement for old address bar list (but should bring to ease of use due to Natural language navigation), while Google search is something innovative and should add up both to productivity and ease of use. Sponsored search is something that is definitely necessary, as it is hard to imagine that Google would give away so much revenue. Eventualy, in this column ad text could be possible, as it might be required by publishers.
And when the user comes to new site, its domain name should appear in access bar, to ensure that user is aware of the site he visits and to prevent fishing.
Finally, this concept should work well with Sidebar navigation, as it has no permanent wide elements (though drop-down is very wide :) ).