On the other hand, if you allow outside communication (such as unrestricted access to the internet), you open the door for "I'll pay someone who already knows this stuff to phone in the answers for me" - which isn't generally an applicable skill in the real world.

As an aside, I hated open book exams - if you were talented and knew the material, you could typically blast through a closed-book examination in half the allotted time and get out of there, while the open-book exams were far longer and more tedious.