We have interfered greatly with Natural Selection. Dogs for example were artificialluy selected by humans for different characteristics. Were polluting the earth at such a rate that many species won't be able to evolve quick enough to survive. Whether or not its a bad thing, I can't really answer. But nonetheless we do play a role.
The first guy who posted is really heartless for saying we shouldn't help the weak and just let them die. I strongly disagree. However government subsidizing and paying people to abort or not reproduce who have genetic history with severe diseases might not be an awful idea. But it doesn't mean we shouldn't help people who have genetic problems who are already here.
Natural selection is what keeps a species genetically strong and from overpopulating. Humans are clearly overpopulated and a lot arent genetically strong. Take children with autism for example. 1 in 50 are born with that condition! That is a lot. If we simply let the weaker ones die off then we'd have much stronger genes and humans themselves. Recall survival of the fittest? Also, because humans value life to much we have to let the weaklings survive. Like people with autism, Down's syndrome, diabetes, and many other disabilities. We develop medical and other methods of letting these people survive, then using resources in them, and in some cases, having their genes passed down and producing more genetically weak. This just keeps spreading and overpopulating this planet with humans. Lots of species of animals leave the weak ones off to die, enabling them to be genetically strong while having enough resources to take care of the strong and maintaining a good population. Humans have valued life to much and failed to do this.
Mate selection IS a part of natural selection. So even on an unconscious level, humans are "interfering" with natural selection. This includes any preference whatsoever for mate selection. If a potential mate is systematically rejected because he was disfigured at birth - that is natural selection. If a mate is systematically desired because of masculine (or feminine) traits - that is natural selection.
When we try to interfere with genetics on a conscious level, I suppose you could argue that we are "trying" to interfere with natural selection. However, this is nothing new. When we domesticate animals -natural selection. When we breed crops for more productive yield - natural selection. Dog breeding is natural selection. When we terminate pregnancies for genetic disorders - natural selection.
I guess people start to get frightened when we start discussing the realities of "designer babies". They feel like now we have crossed the line. They are fearful of the consequences of "playing god". But I think it is just fear of technology. Humans interfering with genetics is an age-old practice, so I suppose it must be a fear of technology because the only time we claim there is a problem with "interfering" is when we might be able to have the technology to know about a potential baby's DNA before in-vitro (thereby having some choice in what sort of traits you want). Even though you aren't ALTERing the DNA, people think this is where to draw the line.
Natural selection is the process by which favourable genes are passed onto offspring, thereby ensuring survival of the fittest. This process occurs naturally over many generations according to what is beneficial within the environment in which the organism lives. There is no way for humans to interfere with such a system.
On the other hand however it is very easy for humans to use a process of ARTIFICIAL selection to 'breed' organisms with favourable traits. We have seen this through the breeding of certain types of dogs or horses that are designed with specific careers in mind. Such species are unlikely to have flourished without human intervention or interference.
There is one final thing to mention which is that there is a good chance that human technology and culture has had an effect on what is now deemed 'favourable', but ultimately this has no bearing on whether humans have interfered or not because this just goes back to natural selection working towards what will be best in the given environment. If humans develop technology that creates conditions that necessitate a certain development in humans then this simply becomes a case of artificial selection.