I love the answers I've gotten so far, but I thought I might as well chime in and describe what I have been doing, since its a little... different.
Generally, I try to answer his questions as best I can... within reason. Many of his questions I can answer fairly clearly, and do so (e.g. Q:"why [is the kitty afraid of me]?" A:"because you're much bigger than her, and you're loud!", or Q:"why [can't I stand on the chair]?" A:"because we don't want you to fall down and get hurt!").
However, for ones that require much more complicated answers that I don't know off the top of my head, are far too complicated for him to understand yet, or for which I simply don't have enough time to launch into a detailed exposition, I summarize it with one word. To this end, I've developed some broad categories of one-word answers that cover almost any situation: "biology", "genetics", "physics", "gravity", "thermodynamics", "special relativity", "chemistry", "economics", and "tradition" are the most frequently used.
I do tend to play fast and loose with some of those (anything involving time gets lumped under "special relativity", for example, even though the topics rarely involve objects in motion), and sometimes I pick one as a silly answer when the "why?" question seems particularly silly (e.g. "stop hitting yourself on the head with your sippy cup!" "why?" "gravity!"; and yes, that's an actual example :P).
We actually started this game with just one catch-all answer of "gravity", which helped set the tone for it as a game, but I eventually decided that having a variety of answers/non-answers was more appropriate and useful. My hope is that the diversity of one-word answers gives him some indication of how much variety there is out there, while also letting him know that I am trying to provide information, but some of it is just too big to convey easily.
This gives me the option of either educating or dismissing, without seeming dismissive, on a case-by-case basis. I do still, on occasion, say "I don't know" when appropriate, but if that is followed up with a "why?" then the answer is invariably "gravity".
It is interesting to see how he reacts to it, as he definitely has favorites of the categories, and it leads to some pretty amusing conversations. For example:
Me: "She [our daycare provider] has a cold."
Me: "No? Not biology?"
Son: "No, daddy, not biology! Thermonynamics!" (I think that was a pretty good attempt for 2 years old!)
Me: (laughing) Thermodynamics?
Son: Yes. Thermonynamics!