This is a tough question. The closest to the road that I've hunted is probably about 50 miles or so. The farthest from the road that I've hunted is probably around 500 miles or so. The last moose hunt I went on, two years ago, we ran a jet boat up a series of rivers and streams a little over 500 miles off the road system.
I read all the above views about the distance between the road and you. However I hunt in a relatively small archery- only area that is riddled with nature trails, roads and fire-breaks. In order to get to one of my favourite sport, I usually walk almost a mile to get there.
Three miles is plenty when you have a deer to pack out! It's surprising how far away from it all even a mile from the road can feel - especially if there are no cut lines or road noise to remind you of where you are.
Seems like most National forests have a road evey few miles, or in each drainage. I tend to hunt areas where the roads are not used much. Most places Im always within 3 miles of a legal road, it just may be a month before someone drives by
Usually 1 to 2 miles in off the most remote forestry roads. These roads are the least traveled where I hunt, but I still like to get further into the elk woods.