No idea in science is as controversial as the theory of evolution. The controversy comes not from within science, but in that grey area where science and religion intersect. This is an issue I've been involved with for many years. Since my late teen years, in fact. I'm part of a group that administers the Talk.Origins Archive, which is probably the largest repository of information about the evolution vs creationism battle on the web. I'm also a founder and advisory board member of Michigan Citizens for Science and have worked closely with the National Center for Science Education for many years.
When Darwin first offered his theory of evolution, with the publication of The Origin of Species in 1859, it was immediately met with a great deal of opposition from many religious groups. Only one year after the publication of his book, scientists and clergy were already dividing into opposition groups and debating the issue. In 1860, a famous debate was held at Oxford between Thomas Henry Huxley (thereafter referred to as "Darwin's Bulldog") and Bishop Wilberforce over the validity of Darwin's theory. But in scientific circles alone, the impact of Darwin's theory was immediate and decisive - within a decade, two at the most, it was rare to find a scientist or naturalist who did not hold that Darwin was essentially right. So what did Darwin actually propose?
The theory of evolution says that all modern life forms (species) are derived from one or a few common ancestors in the far distant past through descent with modification. This was not an entirely new proposition. What Darwin added, primarily, was the explanation for why this occurs - natural selection, acting upon diversity within a population. That basic outline - common ancestry and natural selection - endures today. After nearly 150 years, we have learned an enormous amount about the natural history of life on earth, none of which makes much sense outside of an evolutionary explanation. And while a good deal has changed in terms of the details of how evolution occurs (after all, Darwin did not know what genes were or how they worked, what DNA was, etc), the basic truth of common ancestry remains one of the best supported ideas in science.
Contrary to popular misconception, the theory of evolution does not conclude "and therefore there is no God." Like all scientific theories, it does not mention God at all, or any other supernatural explanation, because such explanations are part of science. They cannot be tested or falsified, so they are immune to disproof and therefore the tools of science do not apply. Most mainstream Christian denominations long ago reconciled with evolution. For a list of religious groups who recognize the vaidity of evolution and see no conflict between this theory and their theological views, see this page.
The opposition to evolution comes from those who argue for a literal reading of Genesis 1, including the idea that God created the universe, the earth and all life on it in 6 literal days. Mainstream Christian theologians, from St. Augustine to modern times, generally dismiss such a literal reading. Indeed, some Christians today argue that not only are evolution and their faith compatible, but further that evolution provides powerful confirmation of their faith. Ken Miller, a Catholic cell biologist from Brown University, has written a powerful book on that position called Finding Darwin's God.
Polls in the US have consistently shown that about half of all Americans reject evolution and favor creationism. But one thing that is clear to anyone who has spent any time discussing the issue with people is that their opposition is not based upon study of the issue but on the notion that evolution contradicts their most dearly held religious beliefs, so it must be wrong. Few people, even scientists unless they're in relevant fields of study, have taken the time to learn what the theory says and the volumes of evidence that it explains so well. They just have an innate sense, brought about by years of having been told this by their ministers and peers, that evolution is anti-God. And they have been helped in that belief by the likes of Richard Dawkins, who compromises his impeccable credentials as a scientist and science popularizer by also being stridently anti-religious. That's fine, of course. I've been known to critique religious views rather harshly myself. But he doesn't bother often to make the distinction between science and the inferences he draws from science. Science is distinct from philosophical inferences drawn from science. For example, take big bang cosmology. Quentin Smith argues that if big bang cosmology is true, God does not exist. William Lane Craig argues that if big bang cosmology is true, it is proof that God exists. So is big bang cosmology theistic or atheistic? Neither, of course. They are each inferring a philosophical conclusion FROM big bang cosmology. The theory, like all scientific theories, says nothing whatsoever about the existence of God. And by the same token, the theory of evolution can also provide different inferences. While Dawkins infers from evolution that God does not exist, Ken Miller and other Christian scientists infer the opposite. I'll let Miller have the last word for now:
It is often said that a Darwinian universe is one whose randomness cannot be reconciled with meaning. I disagree. A world truly without meaning would be one in which a deity pulled the string of every human puppet, indeed of every material particle. In such a world, physical and biological events would be carefully controlled, evil and suffering could be minimized, and the outcome of historical processes strictly regulated. All things would move toward the Creator's clear, distinct, established goals. Such control and predictability, however, comes at the price of independence. Always in control, such a Creator would deny his creatures any real opportunity to know and worship him - authentic love requires freedom, not manipulation. Such freedom is best supplied by the open contingency of evolution.