For a beautiful demonstration of both magnetic force and gyroscopic motion, let's contemplate the Levitron. This novelty toy (which even now sits on my shelf waiting for a quick spin around the block) consists of a magnetic base upon which you spin a magnetic gyroscope. Both the bottom of the gyroscope and the top of the base contain magnetic north poles, and therefore they repel each other.
However, try as you might, you'll never be able to balance the magnet above the base without spinning the top. Why is this?