Probably the most common criticism of evolution is that the order and immense complexity that we see in living things could not have come about through a random process, which they believe that evolution is.
For example, one creationist web site tries to show that evolution is impossible, beginning its analysis with these words:
“You have to understand that evolution is a random process which requires the use of mathematics to analyze its probability.”
Indeed it is true that a truly random process could not allow evolution. The odds against a set of positive genetic changes without any accompanying negative genetic changes are simply too long to be reasonable.
Julian Huxley, the grandson of Thomas Huxley and a distinguished scientist in his own right, once calculated the odds of a horse suddenly appearing as the result of a massive number of mutations without the benefit of natural selection. He conservatively calculated the number of required mutations and then expressed the odds against them all occurring in this way:
"The figure 1 with three million naughts after it: and that would take three large volumes of about 500 pages each, just to print!...No one would bet on anything so improbable happening; and yet it has happened."
Note that Huxley is referring to odds of a horse appearing without the benefit of natural selection. Those odds are very long indeed. (It is worth noting that many creationists misrepresent Huxley’s number as the odds against a horse evolving at all. That’s dishonest. It is actually meant to represent the odds of a horse evolving without natural selection).
It’s not correct to call evolution a “random process”. Evolution is indeed based on random inputs (genetic changes called mutations that occur at random). But those random inputs are affected by a process – natural selection – that is decidedly not random.
Natural selection provides a mechanism for random genetic changes (mutations) that make an organism less well-adapted to its environment to be removed from the population. It also provides a mechanism for ultimately allowing the random genetic changes that do make an organism better adapted to its environment become a part of the population’s genome.
Other processes exist in nature which create apparent order from random inputs. If you were to put gravel containing random sized rocks into a quickly flowing river, it would be sorted by a process called “hydrologic sorting”. The rocks would be sorted such that the larger ones would be underneath the smaller rocks. Waves on an ocean beach do the same thing.
Ironically many creationists use this mechanism to try to explain the fossil record. So, on the one hand they accept the idea that natural processes can perform sorting and create apparent order even when the inputs are random. Yet they reject the idea that a natural process can sort genetic characteristics and they call evolution a “random process”.
 http://www.hauns.com/~DCQu4E5g/DNA.html, referenced on May 30, 2008
 Julian Huxley. 1953. Evolution in action. Chatto & Windus, London, p. 46
 Here’s what Huxley said immediately after presenting his very large number: "Of course, this could not really happen, but it is a useful way of visualizing the fantastic odds AGAINST getting a number of favorable mutations in one strain through pure chance alone...NO ONE would bet on anything so improbable happening; and yet IT HAS HAPPENED.
It has happened, THANKS to the workings of natural selection and the properties of living substances which make natural selection inevitable."