I'm with the both ends people. That is, I start by thinking big, with grand plots, timelines, cosmology, and so on. But once I have a solid idea of the big stuff, I go small, and detail the one area the players will be adventuring in. The thing is, I stick the players in between. So I get the generalities of the world set up, then ask the players what sort of campaign they want to play, they build the local stuff around what they want.
AlphaOmega said:
I remember reading the Dungeoncraft articles that basically said only prepare what you need.
It's more complicated than that. On the one hand, you want to keep things loose. You don't want to get straight-jacketed by something you've already planned, and lead the game into no fun land. On the other hand, you have to take into account what you're good at as a DM. If you're good at ad libbing, you can get away with being loose. If you're not, you need to prepare more, and need a more solid background to work off of when you are forced to ad lib.
As for how much I prepare, when I started my current Dome of Heaven campaign, I gave the players a 52 page handout. After talking to the players, I wrote about 35 pages of adventure material before we started playing. When 3.5 came out, I revised the original handout, which is now 72 pages. I hope to eventually get it up to around 300 pages and release it as a pdf.