Nebulous
Legend
There's clearly a happy medium of prep time to play time. Unless you railroad the players, there's always the chance that your prep goes out the window anyway, so you probably shouldn't do too much (e.g. my players recently choose not to meet two major NPCs for whom I'd done tons of prep, and for whom I was sure I'd dangled enough hooks; fair enough, but frustrating for me). Really, the trick is to think about the game world so that you have a sense of the sorts of things that might happen, whatever (reasonable) path the players will take.
That said, as a player I wouldn't enjoy playing in a game where the DM did little to no prep - I'm pretty sure I would detect it, and it would feel like the world wasn't sufficiently real - (unless the DM knew the world inside-out, either because it was a long-established setting, or because he/she did a great deal of thinking about the world between sessions; for me this counts as prep, even if nothing is written down specifically for that session).
I had recently done a whole lot of prep work in creating a segue to an underdark adventure featuring Return to White Plume Mountain. I had NPCs, a map, the plot hooks, really everything the characters would NEED to follow the path, but the idea of going back underground after such a hard slog through Wave Echo Cave frankly scared them, so they opted for another solution to the problem they had (a cursed character). So ultimately i had to throw all of my prep work out the window and accommodate them instead of forcing them down a path. The NEW path they followed featured a whole adventure into a sewer with vampires, and after prepping that quite a bit, it frankly frightened them to the point that they feared for their lives and opted for another resolution. And i followed their in-game queues and adjusted the story on the fly. Yes, it meant that a lot of my notes and a really nice map were not used.
And this was all done after careful consideration after what i thought they would do, guessing their actions, anticipating possible outcomes, and they still went down a unique path. I'm not complaining, it worked out fine in the end, but it's a good lesson that if you really want the story to evolve organically you have to be ready to adapt and flow with the players decisions.