Some time ago I was going to look at something on the web with my son. He looked on incredulously as I began to type in a (medium-sized) URL. "What are you doing?" he asked "why don't you use the other box?".
I hadn't realized until then that his preferred entry point for everything was the search box. Most 'known' thing he is looking for have a name or some other obvious handle with which to search, and will land near the top of a search. And, the search box remembers what you search for, so most times a single letter will do. Typing in a URL was just too much unnecessary work.
I have been intermittently playing with the new Chrome browser from Google, and it looks as if they have taken on board the experiences of people like my son. They have got down right down to one box: you enter a URL or a search into the single same box and it figures out what to do.
URL and search suggestions are integrated.