Despite the fact they can be warded off by a stuffed dummy on a pole, crows are renowned for their brilliance. In fact, their aversion to scarecrows may be a result of their intelligence. According to the 1881 "Household Cyclopedia of General Information":
The most effectual method of banishing them (crows) from a field, as far as experience goes, is to combine with one or other of the scarecrows in vogue the frequent use of the musket. Nothing strikes such terror into these sagacious animals as the sight of a fowling-piece and the explosion of gun powder, which they have known so often to be fatal to their race.
They likely learn that the presence of a human can lead to a fate involving explosions of black feathers, so they steer clear of even the possibility of interacting with a gun-toting human.
In this video from the BBC show "Inside the Animal Mind," the intelligence of a crow named "007" is put to the test. The bird is faced with an eight-step puzzle to score a food reward. 007 is familiar with the individual objects, but now they're presented together, requiring a certain sequence of steps to unlock the tasty prize.
The crow proceeds to figure it out probably as quickly as many humans we know (myself included).