| I would have to say I am a sandbox DM of possibly the most extreme form. I really tend to get bored of pre-written stuff. the last (and only time in the last 5 years I think) time I ran one I ended up skipping three quarters of the module so I could get back to making stuff up.
The way I tend to prepare for a coming campaign is either read the entry of the village/location the players are starting in, or write that entry if I am running a homebrew. Sometimes I don't even bother with that step.
and then I stop. . .
When the game starts, I generally introduce the village/city/whatever and let the players interact with it for a bit. If the players are not pushing their own agenda I introduce a situation.
This situation (basically a plot hook) is usually fairly minor in the grand scheme of things; A loaf of bread being stolen, an attack on the village, a noble acting arrogantly, you know. the usual stuff. In the last campaign I ran it was finding a diseased and dying person in an alleyway.
Players can get involved or not, I am not phased at all because I just make it up as I am going along. If the players (or a player's) background presents something it gets weaved in as a situation. The key is to make these events seem fairly minor. Many could be classed as pure flavour for the setting. This way, it doesn't seem like I am just throwing plot hooks at the players hoping they will bite. Sooner or later, one or more of the players will be interested in something. Usually this happens quite quickly.
After about three sessions and on average about 4-5 different threads; I spend half an hour or so weaving them, along with anything the players have gotten involved in themselves, together into something coherent.
From this starting point I have had empire building campaigns (based around economic dominance of a war-devastated region and tense negotiations with an orc tribe), a 'free the people from the shackles of feudalism' campaign as well as a political intrigue game amongst the guilds and noble families of a city.
So . . . almost no prep, my notes consist only of the NPC's met so far and a tiny amount of plot.
Despite the simplicity of this, I can create incredibly complex plots. That political intrigue game ended up with about 6 factions (2 of which the PC's were represented in) spanning two empires manoeuvring about who should educate the heir to the throne because of the opportunity to shape the heir's education in ways that would favour one or more factions.
Interestingly, the campaign I am starting this weekend is not going to be sandbox. I am running a module again to see if I can do it!
Hmmm, that was a bit rambly. sorry. | 
And yet another word from our sponsors
