Which cranial nerves are bilaterally innervated?

As I'm sure you're aware, spinal (as opposed to cranial) nerves are contralaterally innervated. This means that a lesion affecting the right side of the motor cortex will affect the left side of the body.

With cranial nerves things are different; those of the cranial nerves that have a motor function tend to be bilaterally innervated. In other words, the right accessory nerve (XI) receives input from both the right and the left motor cortex. The same goes for the left accessory nerve.

This is a handy advantage in strokes, since upper motor neurone lesions must therefore be bilateral in order to cause a deficit.

The one major exception to this rule is the facial nerve (VII). Only the forehead muscles are bilaterally innervated, so even a unilateral upper motor neurone lesion can cause mouth drooping, etc. However, this can still often be differentiated from a lower motor neurone lesion, which will not spare the forehead. This confusing bit of neuroanatomy is nicely illustrated below.

(Illustration by Patrick J. Lynch, medical illustrator)