There may be some controversy about macroevolution -- whether or not all species in the world evolved from unicellular creatures by natural selection. But microevolution, the arising of different traits within a species by the same process, is an observable fact.
For instance, there is a species of moth that likes to rest on white trees. In nature, 90% of the moths are white, and about 10% are black. As you might imagine, the black tenth has it pretty rough -- they are not camouflaged against predators, so they are eaten by birds a lot more often than the white moths.
However, in one region where these moths lived, a factory was built which belched black coal smoke. The smoke settled on the white trees and turned them black. Some years later, scientists discovered that now 90% of the moths were black, and only 10% were white. How did the species adjust for its new circumstances? Simple natural selection. When the trees were black, suddenly the black moths had an evolutionary advantage. Due to their improved camouflage, they were more likely than the white moths to live to adulthood and pass on their genes for black wings to their descendents.
But humans can have a greater role in microevolution than merely providing the catalyst. We can select some plants or animals to reproduce based on the traits we want. For example, the wild dandelion is edible. But it has some flaws: it bolts (goes to seed) very quickly, after which it's much less palatable. It's also very bitter. A relative of the dandelion, lettuce, is domesticated. Humans selected only the slowest-bolting and sweetest plants to reproduce. Modern lettuce has a much longer season than dandelions, and it's mild enough to use raw as a base for salads.
Often, the traits we choose aren't the best for the plant's survival. The bitterness of dandelions makes them less likely to be eaten by animals, and their fast bolting allows them to go to seed quickly, before a rabbit or a lawn mower cuts them down. When we remove those traits, the plant is not as "fit to survive." In the wild, lettuce would quickly be overrun by dandelions. So we provide a controlled environment for our lettuce. Suddenly "fitness" doesn't matter as much as suitability for our needs. We decide to propagate the plant ourselves -- allowing it to shoulder out other plants and become an evolutionary success.
The same goes for fruiting plants. A plant only needs to produce enough fruit to make sure a few seeds will sprout. And it usually doesn't produce more than this, for fear of exhausting the nutrients it has available. But we select plants that overproduce their fruit, so that we will have plenty to eat, and we provide more nutrients to fuel this overproduction.
Our ultimate success has been the domestication of dogs. The actual origin of dogs is lost to history, but it is believed that humans selected the tamest, least aggressive wolves, generation after generation, until we had developed something new. Dogs, then, are actually designed -- by us -- to be our ideal pet. Their genes are much more flexible than most other animals, so that we were able to produce massive sheepdogs, tiny lapdogs, and everything in between. We can breed dogs for guarding, sniffing, hunting, digging, and pretty much anything else. By now we've bred and trained them to lead the blind and assist the disabled.
I recently watched a documentary by Nova called Dogs Decoded, which I found absolutely fascinating. Dogs, it turns out, are instinctively able to read human emotions, and inspect human faces the same way we do -- looking at the eyes first, then moving to the mouth. They can do what a chimp can't -- follow a human's cue to find a treat. The tiniest puppies were capable of learning to find a treat where a human was pointing -- whereas, even with training, wolves and chimps were incapable of this. Many of dogs' abilities would be useless in the wild -- but they are useful to us, so we encourage them and breed the dogs that possess them.
Overall, this process has been extremely beneficial to dogs. Dogs exist in vast numbers around the world, while their ancestors, wolves, are having trouble adjusting to a world with humans in it. Of course, we have to be careful. Sometimes our efforts result in problems for the dogs, like short-faced dogs that develop breathing problems. But this can be avoided with careful breeding and the avoidance of anything extreme.
I just find it so fascinating that we are able to affect our environment so drastically. Man is the one animal that is capable of using tools, but this doesn't just mean stone hammers and bone flutes. No, we can also turn wild grasses into wheat and wolves into companions. We are able to "have dominion" over the earth in a very real way, not as a harsh master, but as a careful steward who tends each creature.
Domestication is frowned on by some, who claim that we are simply "using" animals (and, perhaps, plants?) for our own purposes instead of considering what is best for them. But the fact is, those plants and animals that have been easily modified end up having a new kind of evolutionary advantage: they have learned to live in cooperation with humans. In a world where humans are almost everywhere, that's an important way to be able to live. We care for them, feed them, protect them, and allow them to reproduce. That is what plants and animals need, and, if they could talk, I doubt they'd complain about the symbiotic relationship they have developed with us.