Last session one of my players traveled deep into the fey-wild, into an area that I had not prepared, because I had not anticipated this action. I winged it a bit, and then when he finally reached the heart of the forest, I decided to end the campaign there for the evening. I flat out told my players that I would need time to prepare the next area, because I wanted to do it justice. When you're near the end of the session, that is an easy solution. If it happens mid-session however, you'll just have to improvize. That's what most DM's do... right?
I never feel like I need (or want) to keep my players on a leash. However, I know that when my players visit a new island or city, that I only need to prep that particular location for that session. It is unlikely they'll venture outside of that area. It's not about giving your players "the illusion of freedom", but about giving them absolute freedom, and prepping ahead. And yes, I prep A LOT.
I certainly do. Indeed, great material can come out of this sort of improv. I've had entire campaigns switch direction based on unexpected player choices and my off-the-cuff reactions. I love that element of RPGs.
I experienced this as a player in a recent session of our DFRPG game. A few last-minute cancellations left us without a quorum. On the spur of the moment, the GM added a new section to his dungeon, and we invited my kids to join our smaller group for a side-adventure. This one-off was so creative and fun that it led to multiple new plot threads in the campaign that we keep going back to.