I bought Thinking Physics, by Lewis C. Epstein in 1984. It's one of my favorite books of brain teasers. They are designed to help you gain a qualitative, intuitive sense of physics. The author stresses that after you read each of the many charmingly illustrated problems in the book, you should put the book away and take your time running a simulation of the problem in your head. This is great advice.
The book is broken up into sections: Mechanics (kinematics, Newton's Law of Motion, momentum and energy, rotation, gravity), Fluids, Heat, Vibration, Light, Electricity and Magnetism, Relativity, and Quanta. If you've never seen this book before, you're in for a treat.
Here's an example problem, which I grabbed from Futility Closet:
A tank of water has two holes of equal area, one at top and one at bottom. The top one leads to a downspout, so that both holes discharge their water at the same level. Ignoring friction, which hole produces the faster flow of water?
You actually don't need to know the physics in order to solve this — it yields to an insight.