One of the most horribly misunderstood concepts of all time. It doesn't mean what most people think it does.
Put concisely, here's what natural selection is: The environment will determine which organisms survive to pass on their genetic traits. Thus, the individuals (in the short run) and traits (in the long run) that are best suited for survival in that particular environment will become dominant.
Take note of several things people tend to ignore/forget: if the environment is going to change (such as if it's hot right now and an ice age is coming soon) then natural selection can very easily be detrimental to the population. Natural selection isn't forward-looking, and is not intentional (nature doesn't 'intend' things).
Now let's look at how it can be applies and misapplied to humans.
Gazelle find it quite advantageous to be faster than the lion, and cheetahs are quite happy that they're faster than the gazelle. The most physically fit animals will generally survive, and the population is better for it. Must be so for humans as well, right? Wrong. Wrong on two levels.
On the individual level, being physically fit will likely help you find a mate, but it's far from the primary factor. Yet suppose it was. Would that mean the human species is bettered by having a stronger, faster, more disease-resistant population at the expense of other factors?
It seems obvious that the survival of and quality of life for the human species is not dependent on our ability to run well or lift heavy weights. We don't want to select who reproduces by putting them in the gladiators' arena.
Resistance to disease is another matter, however. Surely having a population immune to Malaria, Influenza, AIDS, Cancer, and Cholera would be nice. But we've already figured out how to prevent these (and most other diseases) with a very high success rate. The only problems are economic (Cholera and Malaria affect primarily poor nations) and educational (most Cancers and cases of AIDS are caused by behaviours known to be very risky: smoking, sun-bathing, unprotected sex with HIV-positive people, &c.).
Economic difficulties are not something to be solved genetically, so such factors can be ignored. This leaves diseases acquired by choice or through ignorance. I think it's pretty clear where this is headed: the trait humans should be promoting is intelligence (used as a blanket-term here: knowledge, wisdom, rationality, thinking power, &c.).
So we sterilise/execute all the stupid people, right? Again, no. Genetics don't play a big part here, and genetics are all natural selection can affect.
Really hugely long ago, the proto-human brain was small, and the people were stupid. Gradually, their brains increased in size, thanks to natural selection. Then, fairly suddenly, the brains stopped changing much at all. What caused this? The development of symbolic language such as we have now. Knowledge could now be distributed easily between members of society. We could learn all we needed to know. The only thing holding us back was that no one knew much to teach us. The education is what mattered now.
This is evident today by comparing intelligent people to Joe Sixpacks. There's no genetic difference between the two, for the most part. You'll have the occasional Einstein with an abnormality, but most geniuses have nothing special but a good education--an education that starts at (or before) birth. (Not by sitting around doing homework, of course, but by being in a happily stimulating environment. We're still working out exactly what makes kids become smart, but we're fairly certain it's the environment.)
In the US, tall people have an advantage, because they get paid more, if for no other reason. This means they can afford nice medical coverage, a house or apartment with a good security system in a nice part of town, and plenty of prostitutes for child-bearing. They have this advantage because they're taller than the average American.
Short people have an advantage as well: they're less prone to heart problems. This advantage is different, however, in that their risk of heart problems is independent of the height of the average American.
Which advantage do you think natural selection will favour?
Given two separate societies, one short and one tall, the short one should dominate. But given a mixed society, as we have, taller individuals will flourish and the society will gradually move towards a taller average height.
Yet the preferred society is the short one. Why is natural selection giving us the weaker society? Quite simply, because the competitive advantage of being taller (and thus richer) is outweighing the cooperative advantage of being shorter (and thus naturally healthier).
Consider this analogy: if an SUV hits another vehicle, the SUV's passengers are more likely to survive than the other vehicle's. If two small cars hit, however, they're both better off than if two SUVs collide. Because of this, an 'arms race' begins, where people try to increase their personal safety by buying bigger SUVs (and hummers). The overall fatality rate will increase because SUV-SUV collisions will increase and SUV-nonSUV collisions will increase. It's a prisoners' dilemma, of sorts.
So what should clever and moral people do if they want to improve the chances of their society (or humanity in general) of surviving? Quite simply, by combating natural selection.