Older driveways that are paved over 10 to 15 years ago. If they show sign of several cracks and undulations: Possibilities are that it is the original, and has never been dug up, and does not have good uniform base of compacted 0-3/4 crushed stone.
Usually there is some gravel base but not uniform in order to give you a solid base. Do not think it has been there in that condition it is compacted. It is not good, the soil acts differentially from location to location. There is a lot of variation on base due to frost movement, when the base is not uniform. Therefore a good uniform base with uniform thickness gives you a better and longer life asphalt driveway.
After all asphalt is flexible in the first year or two and then it becomes hard and brittle, therefore if the base is not uniform in thickness it will crack where it is the weakest and less ground cover. This is all due to soil saturation and freezing and the type of soil. So remember: soil type, drainage, and thickness of the base are very important.
Pavcan will analyze the situation and will recommend what is the best for you. Usually do not go for less than 12 inches of gravel on the base for asphalt regardless of the soil type, but pay special attention to clay and silt base. Since the water does not penetrate through asphalt (it does have permeability but not like interlocking stones).