At the beginning of the exam, briefly look over the whole exam to see how many problems there are, which look hard and which look easy, and how many points they're worth. Just having that knowledge in your head will help you as you do the exam. If the exam is particularly long with questions of varying point value, taking a few seconds to note the point values of each question and marking them off as you do them will help you keep track of how much of the test is left.
Do the easy questions first. These are your surest points, so grab them as your top priority. You may also find that doing the easy questions reminds you of things that you can apply to the hard questions. If the test is essay or short-answer, don't spend too much time elaborating the answers to the easy questions. You can always add more later if you have time left.
If you come to a question that stumps you, just skip it and come back to it later.
On a math test, get there way early, and if there are any formulas or theorems that you have to remember, write them down on scratch paper over and over again in the ten minutes before the test. When the test begins, write them down on new scratch paper. This is almost as good as an "open book" exam or an exam where they allow a "cheat sheet". This also works on exams with essays, where you have to remember various factual points to go into the essay.
Before you go to the test, listen to some music that will stick with you during the exam. This can be quite relaxing and focusing, keeping you in a good rhythm.
Get a lot of rest before the exam. You want to show up both high-energy and relaxed, just as if you were about to do a stage performance or an athletic performance. Anything you can do to prevent your falling into a rushed, panicked frame of mind will help.
Eat an orange just before the test. Ok, this one is a bit silly, but supposedly citrus fragrance reduces trivial errors: http://www.google.com/search?q=citrus+aroma+brain+errors+computer+operators I usually make lots of small mistakes on math tests, but I got my first-ever 100% on a math exam after eating an orange. Coincidence? Tough to say. --Ben Kovitz
Summarize the test material onto just a few pages, notecards, whatever works for you. Review these notes while walking around before the test. It's a half-mile walk through a low-traffic safe residential area, so I review while walking to campus. If this doesn't apply to you, walk around campus.