Depends on the mass of the spider and its ratio to the surface area of its body which, in turn, produces a ratio that determines its air resistance. A smaller spider (or any insect) could survive a fall from many thousands of feet, whereas a South American tarantula probably wouldn't survive your example of a fourth floor window heigth.
An example from Straight Dope involves an insect that is 0.002 meters tall, 0.002 meters wide, and 0.006 meters long and weighs 0.00002 kilograms. He therefore has a surface area of 0.000056 square meters and a mass:surface area ratio of 0.36. This is low enough, compared to air resistance to survive any fall...