Now here's a really counter intuitive one:
As an aircraft goes from climbing flight to level flight at constant IAS what happens to the angle of attack?
Ignoring changes in air density, at constant IAS, AoA is a fuction of required lift. Since we have shown (some disagree) that in climb, required lift is lower, the answer must be:
AoA will increase in level flight.
And yes, it is counter intuitive.
Personnaly, I started suspecting that aerodynamics will never be intuitive to me when I realized that people who say "you climb with power; accelerate with pitch" are right. Now if I'm in doubt, I draw them vector balance diagrams, and write power balance equations. If I can't prove it, then I must say that I don't know the answer.