As soon as we designed medicine and hospitals and artificial body parts and all other sorts of medical matericals, natural selection was killed. The same goes with housing, and clothing, and haters and air conditioners. We have changed the environment to suit us, so there's no longer pressure to adapt.
Natural selection used to weed out weak members of the human race before they were able to reproduce and pass along their weak genes. However, our modern society has enjoyed many technological and medical advances that allow people with physical weaknesses or ailements to survive and even thrive, thus granting them the ability to reproduce.
Natural selection is only slightly possible in today's society. This is possible by means that man has not found a way to subvert yet. Blind cripple and crazy are no longer death sentences in today's society. Neither is it an offense so bad that these people cannot reproduce. The movie "Idiocrocy" portrays this most effectively.
I believe natural selection is still relevant, it just works on different terms than it did in the past. People still end up together today out of natural selection. Arranged marriages are far less common, which means natural marriages are more common. Natural selection still very much exists and is part of daily life.
Of course, natural selection is still relevant. Although people no longer die from the same causes, biological concerns still play a role in who produces offspring. The ability to attract a mate determines who has more children and who spreads their genes to the next generation. It is still survival of the fittest.