I voted for "I plan out most scenes and encounters and fill in the rest on-the-fly", even though that isn't strictly true.
What I do greatly depends on the medium that I'm running the game in, the system that we're using, the feel that I'm going for, the amount of detail necessary for the game's story, and what the players prefer. For example, in your average tabletop session of All Flesh Must Be Eaten, I'll make the zombies and come up with the basic scenario beforehand, then let the players run wild, filling in the details as I go along. Everyone goes into it expecting manic zombie-blasting action, and that's exactly what they get. Good times are had by all with a minimum of planning on my part.
On the other hand, if I'm running AFMBE on a play-by-post site, with an eye towards horror rather than action, I'll plan out the major events of the game before I start recruiting players. PbP games require a greater level of detail on the GM's part, and horror demands a delicate balance of action and role-playing that just doesn't happen in an improvised game. I'll create the fine details while the game is running - play-by-post moves very slowly, so I can create later adventures while still running the current one - but most of it is pre-planned.
The final case is that I'm running a heavy intrigue game in real life. In that case, I have to plan out everything beforehand. I have to know exactly what will happen if X occurs, what villain Y will do if Z is killed before five days have passed, and so on. The villains I run in games like that have incredible intelligence and Machiavellian cunning. Pre-plotting everything that they might do is the only way that I can run the characters convincingly.
But "I plan out most scenes and encounters and fill in the rest on-the-fly" is the closest to the average, so.. yeah. I went with that.
"I think that I think. Therefore... I think that I am!"
- Jack Snipe, in Erfworld