Tests should be open book, open notes, and an extensive amount of time to do the test. The questions should be such that they demonstrate an understanding of the material, not just how well you can parrot back information.
Whilst I would love tests to be open internet, this lends itself to very easy cheating. The material being taught and what notes you take about it should be enough to answer any questions posed to you about the material. Especially those that demonstrate an understanding of the material.