I've always been bothered by this aspect in video games because of their technical constraints. No matter what game I played I never felt like the world was truly open for me to explore. I'd always run into invisible walls or find the immense landscape I was given was not all the fleshed out and a pain to have to travel at times.
This is something I really wanted to change when I ran my first game as a DM. I told my adventurers that whatever adventure they wanted to do, whatever kingdom they wanted to build and rule, whatever foreign lands they wanted to see and discover they could do it as they wished and I would make sure that it was memorable every step of the way.
Of course there's no way in the world that I would take on such a task alone. I gave my adventurers a map of the Nentir Vale and told them that if they wanted to leave that map they'd have to help me make it. Thanks to the fact that we have a topographical master in the party and some very creative members; we often cross in and out of the Nentir Vale at our leisure and the players get to see their impact on the world and the NPCs as they travel.
I feel very accomplished when I hear my players talking over the week about how excited they are for the next meeting because they can't wait for the results of their actions or see how the desert they helped me make turned out. Its great to be able to create worlds like this in Dnd and its one of the reasons why I'll never leave the game or stop being a Dungeon Master.