<p>This is not cheating, as long as the test is not obtained by illegal means. Saving and using old tests that have been handed back to students after grading is completely legitimate. But use at your own risk, the situation in a class may change on you for a variety of reasons (see Tarhunt story above), and the individual who decides to study just by blindly memorizing the old test can wind up hurting bad.
I had an experience along these lines myself: a nutty old professor asked exactly the same questions on tests, year after year after year. The problem was, you really had no choice but to study by memorizing the old tests, since all the questions were also nutty, had nothing to do with the core course material, and could not be answered by applying logic or knowledge, but ONLY by having the stuff memorized. It was much easier and surer to pick up the answers from the old tests rather than having to write down each and every off-handed remark made during lectures.<br>
If you encounter a prof like I have just described, if you can I would advise that you try to find another class or section, even if it seems hard to give up an easy grade. Otherwise, your studying strategy (and what you get out of the class) can be totally subverted.</p>