It's been said by a specialist doctor that any form of mountain descent would affect your knee caps.
Do old mountaineers have knee problems? Is it related to the way you descend?
I'll be sticking to the "Descent and Knee pain" part of the discussion here.
Yeah, there is no doubt that a descent definitely makes knee-pain worse. (I am strictly sticking to the point that it's not caused solely by descending the mountain).
The intensity can vary person to person and that is depending upon habits one has developed over time. Habits here refer to the speed of walking on a descent, Calcium-rich diet, packing sense, load-carrying abilities, etc.
If you go to a physician, He/She will term this pain as Chondromalacia or Patellofemoral Pain Syndrome. These are the most common types of pain around or behind the kneecaps, which is often diagnosed among not only trekkers, but in runners, skiers, and cyclists.
I hope this makes one understand that it's not only because of the Descent. In layman's terms I'd say it's there when you exert your knee, be it in a way with your driving as well sometimes.
The weight/load that you carry, adds more strain to the knees. Period!
A downhill walk with a heavy backpack is definitely a strenuous task for the knees. It's because anecdotal studies say that while descending with each step that you take, the amount of force exerted on you knees is roughly thrice the normal body weight.
The moment you find your knees hurting on a descend, try and keep a steady and a calm pace, need not to rush downhill, if you are carrying excess weight, make sure that the load is distributed in a well manner and see if your fellows can help you with the heavy backpack. Drink adequate water.
If you experience pain on the trail after a hard day of walking, bring along some Ibuprofen/Painkiller or maybe some gel/ointment to reduce the pain and inflammation (if there is any) and stretch your quadriceps before you start again. You may also find that wearing a knee brace/cap is helpful.
You can reduce or avoid knee pain by knowing how to descend properly.
The correct way to hike downhill is not to move your front foot forward and simultaneously load it with your weight at the same time, as most people do. That way, the force generated by your weight (which increases while moving down thanks to the acceleration generated by the movement downhill) will be absorbed by your skeletal chain - ankle, knee, hips, and back. That's a lot of micro traumas that wear and tear the joints.
The healthy way to descend a hill is by far more fatiguing but more effective. You should hold your weight on the back foot as long as you can while moving the front foot forward. When the front foot touches the ground, then gradually shift your weight on it. This way, the above force isn't absorbed by the skeletal structure. It is absorbed by the muscles, which aren't going to be affected negatively that much (they'll actually become stronger after that). This technique requires a lot more strength because by using your muscles as shock absorbers rather than your bones and joints you're fatiguing them, but it's really a saver.
Using trekking poles also helps, by helping in applying the very same principle: transferring some of your weight to the ground through the sticks (thus, your shoulders and arms); this helps unloading the knees from some of the load. The main focus, whether you're using sticks or not, should be how you shift your center of balance on your feet: mostly after you moved the front foot ahead rather than simultaneously.
Sources: The freedom of the Hills book and ten years of hiking experience with former knee problems.
I would say it is likely you can have issues with your knees when you get older as a mountaineer - in the same way someone who regularly runs on the roads can get damaged knees, in this case it is recommended to run on grass (as it's obviously more cushioned) or on uneven ground such as in a forest, which is usually a mix of leaf litter and harder ground - bit harder to do this on a mountain.
Recently having climbed Snowdon my other half has hurt his knee. We're not sure if this was from the climb itself, or a combination of the 7.5 hour climb and the 4 hour drive back home afterwards, so the type of injury itself is not uncommon even in a casual climber.
When you descend a mountain, or even a hill, you put pressure on your knees among other joints. For the most part you can feel this when you're walking down a slope. However there are a few things you can do to help lessen the work your knees have to do. Most people use a trekking pole or two - Are trekking poles proven to be helpful? has some good info on this. Stretching properly before a hike. Resting when you feel the need to. Good supportive boots. Don't overload your pack.
The more you do - in any sport - to look after your body and joints the better you will be in later life. This would however depend on how regularly you climb, what care you take of yourself before and after each climb, if you do any other activities that can damage your knees, etc.
Do old mountaineers have knee problems? I would say not all of them, but if you are likely to get knee problems later in life as a mountaineer, I would say it is possible but not a cert.
I've been a martial artist for over 30 years in a style which puts a lot of strain on your knees, as well as regular cyclist, occasional skier, hiker and ice-skater.
I damaged a knee cartilage and tendons over 20 years ago and have to be careful and have particularly noticed problems hiking.
One thing which has helped a lot is long-term consumption of glucosamine, far more so than regular anti-inflammatory drugs, but that's not enough alone.
Now to the downhill bit.
There are two factors to consider, IMHO, which haven't been addressed exactly by the answers so far.
Firstly, consider the mechanics of going downhill. Apart from the additional impact of descent, consider in particular the leg mechanics. Depending on the slope, your toes may well be flexed forward, "pointed" so the front of the shin is tightened. This changes the geometry of the knee and can cause bits to rub together repeatedly and under more pressure than normal.
You can help alleviate this effect by paying attention to your gait, the rotation of your foot in or out, the alignment of you knee over the foot and if you are tending to be bowlegged or knock-kneed. I think this factor is why knee or ankle braces can help. You may also find that loosening the top of hiking boots, so the ankle can flex forward more, will help.
A related factor is leg flexibility and this is where preparedness and actions during the climb can both help.
For some reason, many people find it hard to relate the flexibility of their muscles and tendons to joint pain (this is an endless argument with my wife, although the lecture from a recently-seen physiotherapist may have ended it :-).
However, when you consider how everything is (literally) connected, if you add tension in the middle between joints it is obviously conveyed through the anchor points.
Sustained effort, particularly if you're not used to it, tends to make muscles tighten up. So, improve your starting point. If you have leg muscles that are so tight you nearly hobble when barefoot, you're asking for trouble. Incorporate stretching into your daily routine.
Then, when you're on the hike/climb, make sure you are stretching regularly. Front and back, above and below the knee. I think you will be pleasantly surprised. It may also reduce back pain if you notice some after a climb.
I've to agree with @Dakatine on this. What also matters is how you descend. The gait and the positioning of the foot matters a lot. I've changed my gait over a period of time to avoid the knee pain. Now, I use more of my thigh and calf muscles. Apart from what Datatine wrote, here are a few more tips to reduce the impact on knees:
Others have already spoken about trekking poles and the zig-zag walks. In both the cases, keeping a bent knee and using the knees as a spring helps.