Creationism is usually thought of as the belief that the creation story in the Bible is true, although other interpretations of the word are possible (see note 1). The problem is that the Bible story doesn't agree with the well-accepted conclusions of science. For a creationist there are two ways out of this problem: first, to deny that science is true; and second, to re-interpret the Bible to make it fit the facts. Both of these tactics are used, with fairly unimpressive results.
Pure creationism makes the following claims: the Earth is young (about 6000 years old), God created all life as it is today, a great flood destroyed life about 4000 to 5000 years ago, the Universe was created according to the description in Genesis. There are, no doubt, many other claims, but these are the major ones, so let's have a look at how realistic they are.
Age of the Earth
Is the Earth only 6000 years old? Well, of course not, which is why many creationists have abandoned the idea and have become "old-Earth creationists". The Bible is sufficiently vague to them that they can reconcile the Genesis myth with an old Earth. But the real history of the Universe which has been uncovered by science still doesn't fit in with events in the Bible, for example we know that the order of creation in Genesis (see note 2) is completely different from that demonstrated by science (see note 3). Maybe the most obvious problem is that the Sun appears well after the Earth and after vegetation. This is obviously wrong (see note 4).
Did God create all life in the forms we see today as creationists (and many other religious people) believe? If this was true evolution would need to be false, which is why so many creationists reject it. Unfortunately for them the theory (see note 5) of evolution is one of the best supported in science (see note 6).
Evolution is supported by two main types of evidence: the fossil record and DNA evidence. The fossil evidence contains many examples (see note 7) of species changing over time and becoming new species (sometimes the fossils of intermediate specimens are called transitional fossils or missing links but this is misleading). Its true that for every species with a fossil record there are thousands without but this is simply because only a tiny fraction of living creatures fossilise. it only takes one case to show evolution happening which means the hypothesis of God creating life in the form it now exists is proven to be false.
Some creationists resort to the idea that evolution only exists in the form of "micro-evolution" where small changes happen but new species aren't formed. There are two reasons this fails: first, micro- and macro-evolution are both the same, they just happen over different time frames; and second, the fossil record clearly shows big changes, not just small ones.
Even if there was no fossil record evolution would still be proved because the DNA evidence is even better than the fossil evidence. Analysis of the genetic material of different species can reveal when one branch split from another, and shared ancestry can be demonstrated through shared genetic sequences. One of the best proofs of shared ancestry (see note 8) are endogenous retroviruses (see below) which are almost impossible to explain without evolution.
A retrovirus infects a cell and, depending on how virulent it is, can kill it. Occasionally, fragments of the virus remain but the cell survives but which parts and where they insert is basically random. On rare occasions the virus infects a reproductive cell so the changed DNA is passed onto the next generation. So if two individuals have the same DNA sequence inserted by the retrovirus they must have come from the same ancestor. This has been observed in humans and chimps proving shared ancestry of those two species (see note 9).
Was there a global flood? Again, the answer is undoubtedly no. Even if a physical mechanism for a global flood could be evoked there is still no evidence it really happened (see note 10). In fact there is conclusive evidence that a global flood has never happened. There are geological formations (see below), records from ancient civilisations, biological remains, and many other phenomena which stretch back in time through the period the flood allegedly happened without any interruption from a flood.
The Green River formation in Wyoming has more than 4,000,000 layers of sediment and each layer would take months to form because the material is so fine. Therefore it clearly shows 4 million years without interruption by a flood. Even if there was no other evidence this would destroy the flood story (and the young Earth), but many other independent areas of science also show the same result.
Some creationists dismiss the Green River evidence by claiming that the layers could be formed over a shorter time, but they ignore the evidence that the layers show seasonal differences (in pollen counts for example) and also longer term changes which fit the sunspot cycle. It is just impossible to refute this evidence which is why the creationists resort to lies in a desperate attempt to support their totally discredited beliefs.
Young Earth creationism has been completely destroyed. There is no evidence at all showing a young Earth but there are thousands of lines of evidence from dozens of different branches of science showing its false. Anyone who still believes in a young Earth is just fooling themselves by ignoring the facts.
Evolution is one of science's greatest theories (see note 5) and its almost inconceivable that it could be wrong. Either of the two main types of evidence (fossil and genetic) would be enough to prove the theory but together they provide some of the best evidence for any theory.
Small local floods undoubtedly happened but there is no doubt that a global flood never occurred. Not only is there no mechanism which could cause it but there is also no evidence at all that it happened.
Creationism is dead. All of the major points creationists have made have been adequately addressed many years ago. Newer forms, such as intelligent design and old-Earth creationism are more subtly wrong, but they're still wrong, so the crap-ometer score is very high.
1. Most creationists believe in a fairly strict interpretation of the Christian creation myth. Other forms of creationism exist but the criticisms made here would also quite well apply to most of them assuming they support religious dogma against scientific observation.
2. This is the order of creation specified in the Bible:
3. This is the order of appearance according to science (numbers very approximate):
4. Astronomers can actually see solar systems forming, and stars (like the Sun) and planets are always formed together. The idea that the Earth might have formed and developed plant life before the Sun appeared is completely ridiculous and contrary to all relevant sciences (astronomy, cosmology, biology, geology, chemistry, and probably many more). But most of the other events are also out of order so the story loses credibility.
5. A scientific theory isn't necessarily anything which is uncertain or subject to likely change. Everything in science can potentially be modified, but well accepted theories rarely are. Therefore it is important not to confuse the scientific meaning of the word "theory" with the more common meaning (which might more correctly be called a hypothesis in the scientific sense).
6. There is really no alternative theory to evolution, which is unusual because there are alternatives and major unanswered questions in many other areas of science. The evidence for evolution is undeniable and comes from many independent sources. See Talk Origins, common descent for details.
7. For a list of transitional fossils and a description of species evolution refer to the Talk Origins, transitional fossils.8. Shared ancestry refers to the idea that all life evolved from one, or a very small number of ancestors. So ultimately all living things are related and the degree to which they are related is proportional to how long ago they separated from the tree of all life.
9. A more complete explanation of endogenous retroviruses is available at Wikipedia, endogenous retroviruses.
10. For a list of reasons why the flood could not have happened refer to the Talk Origins, Noah's Ark web site.
Sources of Further Information
There are many web sites with information on this subject. Below I have shown some which present the information for both sides of the argument.
Wikipedia, Creationism A neutral
overview of the subject.