Wow, lots of interesting conversation going on here. Now, I feel like I need to explain myself a little better. Especially since we seem to be leading into discussions on GMing style. This will be a long post and it will deal much more with my GMing style and how I work to accomodate Free Will into my game. (What can I say, I am extremely verbose.)
First off, for the benefit of Henry and Diaglo - I can spend several hours a week on my character for the game I play in! In fact, there are times when I spend more effort on my character than I do on the game I run. The game I play in has a long story arc that we have barely touched. I rehash clues, I catalog NPC's for future reference, contingency planning on how I can use my character's abilities for various bad scenarios, I plan out probable development in both mechanics areas as well as characterization, we have a webboard that we post to, we have personal and group logs, all sorts of fun. I don't step into Stephen's character on only the nights we game. (Heck, look at my logon name. I chose that name so that my DM would know which posts were mine when he checks the boards on EN World!) So, Diaglo, you aren't the only one spending lots of character time.
Now, that being said ...
I do spend a lot of time on the game I run. I suppose you could consider it "prep time", though some people certainly would not. The current GM'ing style I have adopted is to have several storylines available, but I don't flesh out hardly anything until just before I need it. Generally speaking, my players will default back to these storylines if nothing else has their attention. However, I am perfectly happy to let my players look for new opportunities. If a character wants to do research to try to find a lost tomb to loot .. erm, explore, I will work with them on that. Actually, I love that type of thing! It lets me dust off adventure ideas, old modules, or whatever. I am also happy to bring in story hooks from their character history, past scenarios, or the NPC looking to hire. Obviously, before I introduce any of these, I have a pretty good idea of what will transpire if the PC's "take the bait". Sometimes I also provide incentive to give up a little Free Will.
Example: In the game I run, the Cleric had advanced up a fair number of levels. However, he hardly ever spent any time in his church when he was in town. Eventually, he reached the point where he was the second most powerful cleric of his God in town. He started asking the HP to teach him some of the unusual spells (IMC - Any spell that isn't in the Core books is not automatically available. You have to find a tutor, recover it from tombs, etc.) that he knew the HP had access to. The HP took him aside and pointedly told him that he did not have time to devote to those that took their priestly duties less seriously and did not better the church any. (This cleric hadn't even donated money to the church.) However, the HP did have time to work with the Paladin when the Paladin wanted things. By contrast, the Paladin was very good about checking in at the church to see if he could help out in any way, every time they returned to town. The player got the message and started to volunteer around the church more when he was in town. Eventually, he even volunteered to take on a quest for the Church. That quest was a bear of an adventure for the party.
Did I railroad the game? I would say not. The player chose not to participate in the church and the HP resented having an 8th level cleric around that wanted to use the Temple as a convenience store. Action => Consequence. The player chose to volunteer for a quest and then talked the party into participating. The party grumbled about it, but they went along. Essentially, I was able to run exactly the game I wanted to for that quest. But, the players chose to let me do that. Now, I specifically chose to give them an adventure that I wanted to run and that I thought they would have fun doing. If I hadn't done that, I would have expected a lot of grumbling about my DM'ing. Admittedly, I have been playing with this group for a few years. I have developed a pretty good feel for what they like.
So, they gave up a bit of their Free Will, but it was completely in-character. The Cleric wanted special training from the HP. He worked for it. However, the incentive I provided was based on previous choices of the player. If the Cleric had always been very active in the church, he would have recieved those unusual spells right away. I let the choices drive the game.
But, back to only prepping what I need to. This was a survival technique! Many years ago, I would spend a great deal of time putting together an adventure. I would map out every room, stat out every NPC, all sorts of things. What I found out was that I developed an idea of how the party should proceed through my adventure. Then, if they did something unexpected, I would get very defensive and do everything I could to drive them back onto my idea of the story. I would agonize over these things and my players would end up not enjoying the game as much. It really made me a bad DM.

At some point, I realized that if I let go of that to some degree and stopped investing so much in the details, I could react to changes better.
So, what is the majority of the work I put into the game now? It is almost all in my head. On my way to work, I may be thinking about the personality of the NPC that they party will probably meet. I will try to understand the motives of the NPC. Come up with mannerisms, styles of dress, all sorts of things. If/when I break down and stat out the NPC, it is really easy! I take the idea in my head and convert it to stats. I actually take a notepad with me to lunch many times. I can often stat out the majority of the NPC while I eat.
I may think about the storylines I have out there for the PC's to participate in. I can fine-tune these ideas. I can advance their timelines, figure out what resources might be needed for the vile plot to overthrow the world, whatever. If it is a storyline that the PC's have not engaged themselves into, I can decide what "news items" might come out of the advancement. Maybe this will get the PC's attention, but if it doesn't, it still makes the game feel alive.
If I know the PC's are getting to a lost tomb, haunted ruin, hidden cult hideout, or whatever, soon, I will begin to think about what the place looks like. Then, when I put pencil to paper, the layout comes very rapidly.
The key, for me, is that all of these things are fun for me. It is also something I can do when I am anywhere I can think. It also means that I know what is going on around the PC's, so if they do something unexpected, I can roll with it and wing it for a bit. I suspect that all of us do this to one degree or another. But, I used to rush to paper too quickly. I wouldn't consider all the options and I wouldn't even spend as much time trying to engage the player's interest with a strong story hook. I had a cool idea and I wanted to develop it completely. Once I did that, I began to have an "investment" in my work and I would feel bitterly disappointed if the players didn't like it, or if the deviated from the course I imagined.
By adopting a different style, I run a much better game. I asked one of my players about how much Free Will I give them in the game just last night. I was curious what his take on it would be. He thinks I give them complete Free Will and if a character can come up with a good enough reason, I will let them do anything. Frankly, I was a little surprised at his answer. I didn't think that was quite true, but I do take it as a compliment. I had asked the person I felt would be most likely to respond on how I have not allowed Free Will. I mean, I do have multiple storylines that are moving forward in the world. Even if the PC's are not participating in them. This player knows that. They seem to like the feeling of being able to choose to work on thwarting those nasty storylines, or going and doing something else.
I do try to determine what my players want to do next. I listen to their conversation and I talk with the players afterward. I try to get a lot of feedback on what they are enjoying, where their character development is going and what their plans are. This gives me better "food for thought" during my mental prep time.