This happens when the axis of the "mapping cylinder" is not aligned with the axis of the cylindrical shaped object that you are trying to map.

In the sequence below I selected only the side faces and then hit "Cylindrical Mapping".
One can clearly see the two are not aligned.
On the one end you will see a red T. Click that and that will give you access to the transformation manipulators of the mapping cylinder.
By default you get the "move manipulater". Hit the blue circle and you get access to the rotate manipulator.
Rotate until it aligns.

But there is also an easier way. If you have construction history enable, just go into the inputs of the polyCylProj and change the rotation values.