1. In general, I'm more the storytelling type of GM. Doesn't mean that I'm prone to railroading (quite the contrary, in fact), but to me, role-playing is mostly a type of collaborative storytelling, which I think lends well to PbP games. Also doesn't mean that I'm the storyteller, and you're the listeners. I expect you to tell the story with me.
2. I value the input of players. Be it in the form of background stories, in-game or out-of-game suggestions, if you offer me hints at what you like to see in the game, I try to include it. That also does mean that I don't feel slavishly bound to an AP's plot. Sure, that is, why we have met here, so we'll try to get the AP done, but if it shows that there's something to explore out of the AP's direct scope, as long as you want to, we'll explore it together and return to the AP's plot later. (just as an example, I read Iolaire's background story and already think that it would be a bit unsatisfying not to include it into our story one way or another).
3."Think the rulebook has all the answers? Then let's see that rulebook run a campaign!" Mike Mearls said this and I totally agree (I could also quote Monte Cook or Gary Gygax to the same effect).
That does not mean that I don't value the rules, it especially does not mean that I cheat (I don't and I won't). But it means that I don't invoke rules just for the sake of rules-lawyering and thereby break the flow of the storytelling, when it isn't necessary. So if you want to climb over a wall, I may not necessarily call for a climb check (You're naturally free to still do it). This said, I may use failed skill checks a bit different to what's the sandard in D&D/Pathfinder and instead use them as in "well, you still succeeded, but (insert interesting, possibly nasty side-effect)."
