Our browsers are dumb, and encourage 'search'. Google's made inroads by making a faster browser that makes it easier to 'search' (through them, of course), but keeping track of that information in the browser sucks. Browser bookmark tools are a joke, and web-based ones, while better, generally aren't much better.
I envision a 'browser' that can track my behaviour, watch what I do, show me more detailed history info, make 'history' part of my 'search' results, adapt my search to my behaviour and more. Perhaps Google will be the ones to do this, but they'll only do it if they can show us more ads (or "more relevant" ads).
Ideas: "history" on chrome, for example, shows me a little information on pages in my history, but not too much. Did I copy/paste information from that page? How long was I on it? Show me thumbnails from that page. Show me other meta data from that page (author, friends that shared it on facebook/g+, etc). Information on what I did with info on that page is often what I'm looking for, not just every page in my history with a particular word on it. Screenshots would help jog my memory, but so would something that said "you copied 'foobarbaz' from this page and emailed it to sam" next to a history result.
Merging in local bookmarked and historical pages in with regular search results. Or, more to the point, merging in external search engine results when I'm searching through browser history. Have an option to make searching my local history the default, with extras merged in from google/bing/yahoo/etc.
None of this will happen overnight, but... there's a huge amount of metadata associated with the activity with page data that isn't being used, because having us go to a browser bar and search (again!) for the same data we found 2 hours ago is more profitable. Our browsers are dumb right now, and there's quite a lot more that could be being done to take advantage of the local intelligence that lives on our desktops or in our devices.