Push-ups are one of the oldest and most used for exercises. They are important for working one's abs, but they can also be very useful for the triceps and shoulders.
Push-ups can be executed regardless of where you are, and they are completely free too :-) and require no special equipment or machinery. All you need is the ground and your body. These exercises are excellent if you are looking to develop your upper body, but you will also find that with proper execution, your abs will flatten as well.
How to do push-ups, and the correct way of executing them: