Skiers bend their knees to be close to the ground while skiing. Why do they do this?

Lower the center of gravity to make turning easier
Makes it easier for the legs to absorb bumps.
Reduces frontal area to lower wind resistance for increased speed.

1) "By simply bending your knees, you can “unweight” yourself! See it with your own eyes! All you need is a bathroom scale.

Here’s what to do:
1. Stand up straight on the bathroom scale and take note of how much you weigh.

2. Lower yourself quickly by bending your knees. What happens? After bending your knees, what did the scale read?

3. Now try the opposite. After standing on the scale for a few seconds with bent knees, quickly stand up straight. What happened this time?

Explanation:
As you quickly bend your knees, for a very brief moment, you actually “unweight” yourself. In other words, your body’s weight is no longer on the surface on which you are standing—in this case, the scale. When you move your knees quickly, your upper body loses its support, causing it to fall through space—thus experiencing “weightlessness” for a split second.

When you quickly stood up straight after having your knees bent, the force of your body hitting the scale is so great that you suddenly “gain weight” momentarily.

This is why you see skiers, skateboarders, and snowboarders bending their knees. Even if you’ve never participated in any of those sports, you’ve probably “unweighted” yourself before. Think about a time when you accidentally stepped on something sharp. You probably bent your knee, dropped your hips and rushed your other foot forward to support your weight. In doing so, you reduced the force holding your foot against the sharp object. In other words, you “unweighted” your foot!"
Source and further information:
http://www.carnegiesciencecenter.org/Default.aspx?pageId=290


2) "Knee injuries account for 30% to 40% of ski-related injuries each year, says orthopedic surgeon Kevin Plancher, a New York surgeon and an official doctor for the U.S. Ski and Snowboard teams. One of the most common knee injuries is damage to the ligaments.

Many people are not accustomed to using their knees as "shock absorbers," which is their main role in downhill skiing and snowboarding, says Mark Purnell, an orthopedic surgeon in Aspen, Colo., and U.S. Ski Team physician.

A lack of strength and flexibility in the knees — as well as back and shoulders — can contribute to injuries, he says."
Source and further information:
http://www.usatoday.com/travel/destinations/ski/2007-12-30-ski-fitness_N.htm


3) "Every skier and snowboarder has heard it more than once in their life: "Bend your knees." That's particularly good advice for tense beginners or intermediates who look rigid. But what appears to be "knee bend" in experienced skiers and riders is actually a kind of functional relaxation, something that becomes a habit in all good athletes because of one important fact: Relaxing the knees facilitates balance."
Source and further information:
http://www.fitter1.com/About/Articles/bulletproof.aspx


4) "Positioning your weight:
Probably the biggest obstacle to skiing well is having one's weight in the wrong place. The next time you go skiing, spend some time watching other skiers - preferably from the side of a run. Notice how they position their bodies over their skis. Watch a beginning skier. He will most likely ski with his butt far too back. Now watch an advanced skier. He will stand relaxed, knees slightly bent- his body almost perpendicular to the hill.

The difference is in the center of gravity! To achieve optimal control, your weight must be on the leading surface of both skis. You should have as little weight as possible on the tails. By having your weight forward, you have your leading ski edges in full contact with the snow surface. The fronts of yours skis, when properly weighted, is where the control comes from.

Make a concerted effort to maintain your weight on the balls of your feet. Don't ski flat-footed, and definitely don't ski on your heels.

The moment you stand on the balls of your feet, your weight will shift forward. Try this little test right now. Stand up with your feet flat on the floor - the way you would normally stand. Note how your knees feel locked slightly backwards. Now, shift your weight forward onto the balls of your feet. Notice how your center of gravity shift slightly forwards. Notice how your knees unlock and your heels lift off the floor. You are now in the correct posture. With your knees slightly bent, your legs are ready to absorb any shocks created by skiing on uneven snow. Your weight is forward...which forces the front of your skis into the snow."
Source and further information:
http://www.skinc.com/ski_tips.htm

Lower their center of gravity

many reasons, and good answers here it is all about control of the skies with 4 skills balance, edging, presure, rotery. as already stated in other answers bending knees helps balance and presure by working as shocks, it also increases the amount you can roll on to your edge and since the majority of all the rotary movment in your leg is generated from your hip socket and transmited by your femur it is necessary to bend your knees to alow the femur to swing as a lever. bones are the levers muscles use to transmit and amplify movment

It is to reduce the air resistance as they speed down the slope.

Centre of gravity has nothing to do with it as this would only benefit the skier when he/she takes corners but the skier is travelling at such speed that he/she needs to stand to counter the centrelpedal force pushing the skier out of the corner.