Pilates is an excellent exercise discipline that develops strength and agility, and you don't need to take formal classes or use Pilates machines to get its benefits. Using a stability ball with floor exercises is tailor made to target your core -- the muscles of your abdomen.
Here are three to try from the American Council on Exercise. Note: Choose a ball between 7 inches and 10 inches in diameter.
Roll-ups: Sit on a mat and place the ball between your legs. Raise your legs and slightly lower your back to make a V shape with your body. Your arms should be straight out in front of you. Now, keeping your legs elevated, engage your pelvic floor and abdominal muscles and slowly roll down your back, vertebra by vertebra until it's flat on the floor. As you go, your arms reach up and behind your head until they're flat on the mat. Touch the floor briefly and then roll back up. Build up to 10 repetitions.
Leg Circles: Lie on your mat and place the ball under your right calf, just above the ankle. Point the toes of both feet and then make sweeping circles with your left leg, lifting it up and out to the left in a counter-clockwise direction. Repeat 5 times and then reverse to clockwise. Next place the ball under your left calf and repeat the exercise with the right leg.
The Hip Bridge: This exercise is similar to yoga's bridge pose, while engaging leg and core muscles. Lie on your back on your mat, knees bent and feet flat. Place the ball between your thighs and bring your arms behind your head, palms up, as you inhale. Exhale and lift your hips off the mat into the bridge as you sweep your arms to a forward facing position at your sides. As you inhale, lower your hips and move your arms back overhead. Do a set of 10 repetitions.
Remember to keep your core engaged at all times -- and have a ball!
The American Council on Exercise has more on these and other exercises to do with a stability ball.