I haven't attended law school, but I've self-studied a few of the casebooks and readers they use, and most examples are contemporary. In fact many profs and book-writers go out of their way to use examples their students will find relevant/entertaining. Sometimes that even gets them into trouble; in a recent case, a law prof was suspended for posing a "colorful" hypothetical about shooting his dean in various combinations of circumstances: http://volokh.com/2011/02/16/criminal-law-professor-suspende...
I have never had a law exam question that tested something on outdated law. I'm a third year Cdn. law student but it's probably quite similar.
The old cases are taught because they're still relevant to some principle. A 1600s case about a music hall burning down sounds ridiculous until you realize that "buildings burning down" is still a problem that exists today and that's the origin of the doctrine of frustration.
