Any serious mountain range (e.g. Alps or Pyrenees in Europe), if you are good enough in mountaineering (it looks on the surface like everything is inhabited, but there are huge patches of mostly untouched wilderness everywhere). However, you have to be in a pretty good physical condition and have some training to do that, which is probably not the case for most HN readers, including myself :)
I really like to hike in Alps, but I don't know how to find these uninhabited places. For sure there are things for more experienced mountaineers, but on these routes there are also people, just more experienced ones.. Besides, I don't want a technically difficult route, I want a route without people..
You don't need to go to an exotic place, there are significant wilderness areas all over the US (eg. Boundary Waters in Minnesota). If you choose less traveled areas, there's a good chance you can go a week without seeing anyone.