The following is an excerpt from:
http://www.fitnessusa.com/Balance.htm

Balance is the most overlooked element of fitness and should rank right up there with strength and endurance, but gets overlooked until you have a problems. Various sports activities can call for good balance and we're all aware of the susceptibility of seniors to falls.

Balance is controlled by an array of body systems that track sensory information from nerves and muscles. In older people, balance may worsen, because they become less fit and sensory receptors begin to fail. An improvement in balance can benefit everyone and make you feel more graceful and improve coordination and posture.

Staying as fit as you can will help preserve your sense of balance, but here are some specific exercises to add to your workout.

1. Stand near a support, rise to your tiptoes 10 times. (Repeat with your eyes closed)

2. Stand on one leg, flexing the other leg slightly. Repeat 10 times.
(Repeat with your eyes closed)

3. Repeat exercise #2, but lift your leg to the side. Repeat with the other leg.

4. Stand in a heel-toe position (right foot ahead of left foot, with toes touching heel) (Now try it with your eyes closed)

5. Practice walking heel to toe across the room. (like walking a "tightrope")

6. Repeat exercise #5 with your eyes closed. (Now try it again backwards)

7. Stand on one foot and lean forward to touch the ground with your hand, without the other foot touching the ground.

The previous answer is excellent but there is another thing you can do.

Good shoes with good support will not only improve balance but will lessen
the added stress your body is coping with as it tries to maintain proper balance.
If the loss of balance results from nerve damage and/or muscle weakness, keeping fit
is important but overlooking the role of a good shoe will add to an already bad situation.

This means never wearing sandals or cheap shoes, rather a shoe that gives support to the ankle area. Invest in one or two pair of very good shoes and you will see a huge difference in balance.

There are so many brand names out there to choose from. You will immediately feel a difference if good shoes are part of your daily routine for balance improvement.

I speak from experience on this one :)

Take yoga classes and/or pilates (especially if you use one of the big pilates balls you can sit or lay on).

My favorite yoga postures for standing balance are the tree and the eagle. You can find more information about them and other poses online or from yoga books if you don't have the time or money for a class right now.

With a pilates ball you can lay on your stomach , starting with your hands and feet on the ground, and then extend your left arm and right leg. Then, switch sides.

Study Tai Chi