Evolution.
I'm afraid that I'm about to go on a bit of a pedantic tear, but a rather interesting post by naamaire inspired me to do it. It has come to my attention that many people, particularly those who subscribe to Creationist models, seem to misunderstand completely how the theory of evolution works. Those more knowledgeable than I about evolutionary biology may add information in the comments if they wish; I think that such a thing would be most useful.
I apologize for any incoherency, as well as typographical, orthographical and grammatical errors. It is late, and I am tired.
Many people misinterpret the theory of evolution; they seem to think that it has something vaguely to do with monkeys, or that it involves elephants' giving birth to hippopotami (or any other combination of a species giving birth to another). Those are gross oversimplifications; that is not the way in which evolution works at all. The theory of evolution describes gradual changes (and when I speak of gradual changes, I am speaking of changes that very well may take millions of years) in organisms that allow them to adapt to their environment. A dramatic change, like the elephants' giving birth to hippopotami that I gave in my example, would actually be antithetical to what evolution posits.
Organisms evolve through mutation and natural selection. Genes do not always copy themselves perfectly from parent to child; sometimes they mutate for no apparent reason. If the mutation happens to be adaptive, then the organism that harbours the gene will pass it on to its children, and if it is maladaptive, then the mutation will generally make sure that the organism does not live long enough to reproduce; therefore, such genes would not be passed on to the children. This would go on for quite a long time, making it very possible for new species to come about.
I should give an illustration so that my readers can understand better what I am talking about. I am sure that most of my readers are well aware of insects that evolve to be resistant to insecticides. When farmers apply such insecticides to their plants, those insects who happen to have (for whatever reason) a greater resistance to the pesticides will be more likely to survive and reproduce with each other, giving rise to more insecticide-resistant insects. Those who are not resistant will die. I know that many creationists will stop me there, and will try to call such evolution 'micro-evolution', which they admit exists, but will call larger-scale evolution (which is simply more 'micro-evolution' over a longer period of time) 'macro-evolution', which they dismiss. This is a fallacy; species tend not to come about during the course of human lifetimes. In fact, humans have been on Earth for rather a short time and have not had enough time to observe evolution directly, especially for large and complicated organisms like ourselves. Large-scale evolution does not happen in an instant. That we can see the sort of evolution observed in these insects is remarkable as it is.
The idea of organisms' suddenly giving rise to a newly evolved form and the argument about transitional forms' not being found are both utterly preposterous. Scientists do not believe this, and I am sure that they do not expect laymen to believe this, either. Of course a species only gives birth to its kind! It would be foolhardy to assume otherwise. Evolution's gradual nature, discussed earlier, makes that extremely improbable. Regarding the question of extant transitional forms, Richard Dawkins discusses transitional forms in an essay entitled 'Gaps in the Mind' in his book A Devil's Chaplain. He gives an example of transitional species in the form of the Herring Gull and Lesser Black-backed Gull ring.
The best-known case is the Herring Gull/Lesser Black-backed Gull ring. In Britain, these are clearly distinct species, quite different in colour. But if you follow the population of Herring Gulls westward round the North Pole to North America, then via Alaska across Siberia and back to Europe again, you notice a curious fact. The 'Herring Gulls' gradually become less and less like Herring Gulls and more and more like Lesser Black-backed Gulls until it turns out that our European Lesser Black-backed Gulls are actually the other end of a ring that started out as Herring Gulls. At every stage around the ring, the birds are sufficiently similar to their neighbours to interbreed with them. Until, that is, the ends of the continuum are reached, in Europe. At this point, the Herring Gull and the Lesser Black-backed Gull never interbreed, although they are linked by a continuous series of interbreeding colleagues all the way round the world. The only thing that is special about ring species like these gulls is that the intermediates are still alive. All (Dawkins' emphasis) pairs of related species are potentially ring species. The intermediates must have lived once. It is just that in most cases, they are now dead.
Richard Dawkins, 'Gaps in the Mind' from A Devil's Chaplain, p 22
Dawkins' example says it rather clearly. Transitional forms do exist.
I hope that this little write-up serves well in explaining how evolution works. If anyone has questions, do ask, and I shall either answer them myself, or point you to something that would answer the question for you.
Further reading
Richard Dawkins' The Ancestor's Tale
Richard Dawkins' The Blind Watchmaker
Daniel Dennett's Darwin's Dangerous Idea
TalkOrigins.org