Since the wind does other stuff beyond just feeling breezy, it stands to reason that there exists some level of wattage we could pull out of it that would have undesirable effects.
If there were no wind tomorrow, we can agree that this would be bad. Are there lower levels of energy depletion where the effects would be subtler and harder to anticipate? Would pulling 0.5% of the wind's energy result in shifts in weather patterns, even if it's localized?
I mean, since we're collectively so good at breaking things, maybe it's worth assuming we will fill some hypothetical area with as many contraptions to take energy from the wind as we can, and that these contraptions will get increasingly effective.
EDIT: There are some great replies to this, and the minds of HN are always an awesome resource to tap. I guess I can't shake the vague spooky feeling I get from interfering with a massive system that feeds into itself in unpredictable ways, but it sounds like ruthless expansion of some massive drain on the wind system is unlikely/impossible.