Yeah...I think I'm pretty much in the "maybe" club.
I am more than willing to say "yes"....I am more than willing to say "no."
The premise of the original thread is MUCH too broad, IMHO. It really...totally...depends on what the request is! I don't have a "default answer."
A question about allowing this or that background, NPC family member or something like that? Most likely a yes.
A particular skill or ability from this or that splat book...Possibly. I have to look at it.
A non-setting race or non-setting class...most likely, a flat out "no" if not a "Well we can, with this particular caveat"...which I suppose would count as a "yes, maybe."
As others have pointed out here, if it goes against a prescribed setting...and I DM in my own long-established and well-detailed prescribed setting....oftentimes there is a "no" or a "yes, but".
At the same time, I have gotten players well out of the habit of requesting "out of setting" or "out of approved material" things simply by the plainly stated fact, "If you bring it into play, then it is fair game for ME to use! BWAHAHAHAHA." <ominous thunderclap and flash of lightning>
This, generally speaking, is enough to make the player who thinks he's getting something "by me" or "improving his character beyond anything the world can handle" to decline the approval.
EDIT: Also, from the DMing perspective, one MUST consider that fact that if you allow X or Y for one player, then X or Y is a valid option for ALL players. So the question really isn't "What's your default answer" but "What can of worms are you willing to open?!" /EDIT
Jus' sayin'.
--SD