Parallelism is a difficult position to hold, since it does little to account for the fact that the brain and mind seem to regularly interact, and that changes in one appear to affect the other. If the two are separate substances in a dualist view, then the idea that there is no causality between them, yet obvious changes in both simultaneously, seems counter-intuitive. For this reason it is not a commmonly held belief, but merely a presentation of the third possibility, the others being two-way interaction (as in interactionism) and one-way interaction, as in most forms of physicalism.
Although Leibniz was a monist, believing that only one true substance exists, he presented a form of parallelism in his theory of mind. Leibniz states that although they are of the same substance, the distinction between mind and body is a useful one for the purposes of understanding and explanation. He held that they are not causally related, but that they follow the same path which has been previously arranged by God. Leibniz's theory is known as pre-established harmony.
See: mind-body problem