The question of doing the "plank" exercise recently came up and I was quick to acknowledge that I do indeed do this exercise, including a number of other core muscle exercises. I believe that core strengthening exercises are crucial for martial artists as it improves your anatomical structure and posture, support the spine and therefor may reduce back injuries, and generally improves balance. Movements of the limbs are most efficient when the core is strong and stable. Apart from the value of improved balance, in Taekwon-Do the effective employment of the muscles around the abdomen and waist in power generation cannot be understated, and core muscle strengthening definitely helps towards this. On a personal note, I injured my back many years ago and I find that core muscle exercises together with back stretching and good sleeping posture helps to relieve the occasional onset of back ache.
So here are some of the core muscle exercises I do. Start by keeping each position for 30 seconds and as you get stronger, work your way up to a minute or two minutes. You may fall over in many of these postures, so make sure your environment is clear of objects that may cause injury were you to fall on them.
Plank (with variations)
The plank is one of the most popular core muscle exercises. It is basically a variation of the push-up position, but instead of doing actual push-ups, just go halfway and keep it there. Try to keep your body in a straight light -- don't lift your pelvis up, neither let it drop towards the floor. You may keep your hands shoulder width apart, or closer (as in the picture) to get variation in the exercise.
Once you feel comfortable with the regular plank position, have your feet and hands shoulder width apart and then lift one hand off the floor. Keep it in the air for 30 seconds, then alternate. Next move onto the superman plank. For this exercise lift one foot and the hand on the opposite side of the floor. For instance, raise your left leg and right arm, so that you balance on your right foot and left hand. Keep for 30 seconds and alternate.
An easier superman plank keeps one knee on the floor, rather than just the foot.
Side Plank (with variations)
For the side plank, position yourself on your side and lift your body off the floor, balancing on your fore arm and side of your foot. Try to keep your body in a straight line. Do not let your waist drop towards the floor. As you improve in strength and balance, raise yourself onto the palm of your hand.
When your balance and strength have improved adequately, try the starfish side plank as in the picture below, by raising your top foot and hand towards the ceiling.
For an extra challenge, you can try the starfish side plank with hamstring stretch as in the picture below.
For the V-Press, balance on your buttocks, and lift your feet off the floor. Try to keep your back straight, so that your back and thighs form a "V"-shape. Keep your arms and lower legs parallel to the floor.
As your balance and strength improve you can increase the difficulty of the V-press by straightening your legs and arms.
As you become adept at these exercises you are likely to notice a general improvement in your balance. You may also notice how other exercises seem much easier -- for instance you may find that you can do more sit-ups and crunches and push-ups and even some kicks may seem easier.