Laboratory experiments: Bacteria are usually the subject of laboratory experiments involving evolution because they can reproduce very rapidly, with two or three new generations appearing every hour (rather than every 20 years or so as with humans). Richard Lenski's experiments for example, have allowed 'irreducible complexity' to be observed developing by Darwinian processes in E-Coli bacteria, in experiments that have been running for decades and that can reliably reproduce their results (Footnote: Proponents of intelligent design argue that a system which has inter-dependent parts and cannot be simplified without losing its function [that is 'irreducibly complex'] is impossible to explain by Darwinian processes. The Lenski experiments are one way to prove that this is not the case.). Nylon-eating bacteria have evolved recently which produce three different types of enzyme that are only effective at breaking down nylon by-products (nylon was only invented in the 1930's), and are unlike any other species of bacteria - they have specifically evolved the ability to digest nylon due to the man-made production of nylon - and scientists have been able to force another species of bacteria to evolve this ability, by restricting available nutrients. Various bacteria and viruses are known to constantly evolve resistance to antibiotics and vaccines through Darwinian processes (the individual organisms that are better able to tolerate the treatment are the ones who survive and pass on the advantage to their descendents, making the treatment ineffective).
Observation: With speciation (the development of new species) typically taking place on the scale of millions of years, it is not possible to observe large scale changes as they occur due to our comparatively miniscule life span. Even so, speciation has been observed in the wild. The London underground has a population of mosquitos that has evolved in the tube tunnels, isolated from their above ground ancestors, and now considered a separate species (it is almost impossible for them to reproduce with their above ground ancestral species, and they exhibit unique behaviours).
Perhaps the most spectacular example of observed evolution in the wild is that of Italian wall lizards. In 1971, a small population of lizards were deliberately transported from one island to another. Nearly 40 years later, it was observed that the descendents of this population had evolved to adapt to the new environment. The new population had a much higher amount of vegetation in their diet, and had developed larger heads with more bite force and new, less territorial behaviours. Most striking of all though, was that the new population had evolved an entirely new feature: cecal valves (sphincter muscles which separate the small and large intestines to prevent colonic reflux, slow down digestion, and provide fermentation chambers for digesting plant matter). Just a few decades is incredibly quick for such a sophisticated new feature to evolve before our eyes.
Comparative morphology: The physical structure of different species also shows strong indications of evolution and common descent (this includes homologous structures, where different animals use the same body part, sometimes for different functions, and analagous structures, where different body parts are used for the same functions). For example, all mammalian tetrapods (four-limbed mammals) have a hand or forefoot with the same number and arrangement of bones, but a bat's hand has been modified to act as a wing - the bones in a bat's wing are fingers and are identical in number and arrangement to those in other mammalian hands (albeit elongated and reduced in density), because the bat's wing is a hand (not originally designed as a wing). Similar re-arrangements of existing body parts are seen throughout the animal kingdom - exactly as one would expect from the evolutionary model (but unnecessary and counterintuitively restrictive for something specially designed). There are also cases where environmental pressures have led to the evolution of similar structures from different body parts - such as the tail of a whale or dolphin, which is horizontal due to evolving from land mammals, not directly from fish, and is analagous to the tail of a fish or shark (which is vertical).
The recurrent laryngeal nerve (which runs from the brain to the larynx) shows evidence of an evolutionary past - in fish, these nerves run in a direct route from the brain, past the heart, to the gills. In animals that evolved from fish, as the heart moved lower down the body, and the neck formed, the nerve had to take a detour - it cannot just break apart and re-form in a direct line, so it had to lengthen. In the case of giraffes, this means that the nerve makes a detour of over four and half metres! The nerve runs from the brain, down the neck, round the aortic arch (near the heart), back up the neck, to the larynx - completely unnecessary if the giraffe was specially designed, but in reality an unavoidable relic of evolution due to its ancient fishy ancestry.
Geographical distribution: Where a population of animals becomes isolated from other members of the species, the evolutionary model predicts that they will evolve to fill whatever environmental niche they are isolated in. Geographic isolation can occur with the formation of islands, where a population is accidentally transported from one island to another, or where some other geographical feature such as a river or volcano causes a long-lasting separation of a group. It was comparison of the fauna on different islands of the Galapagos that helped Darwin develop the theory of evolution - local populations adapt to local conditions and develop new traits. When an island is separated from the mainland for an extended period of time, the evolutionary path diverges much further - hence there are so many creatures that are unique to Madagascar, or unique to Australia - they are unique because they evolved there in isolation from their ancestral populations. Such an exact fit with evolutionary theory does not make sense for special creation (unless the creator wanted to make it look like the creation had evolved), and also presents a problem for the biblical account of a global flood (since animals would need to be teleported to and from their native islands - more on that in the next chapter).
Genetics: Studying the genetic code of different organisms allows us to trace family lines where different species are related. Mutation rates can be observed and corresponding predictions made about evolutionary timescales and relationships which can then be verified with the fossil record and comparison with extant species. There are key markers in genetic machinery, including copying errors, which prove a common ancestry.
Certain retroviruses will infect a creature and actually alter the DNA sequence in its cells (all viruses use the host's cellular machinery to make copies of themselves, but retroviruses actually leave behind a copy of their genes in the host's cells). When this happens in a reproductive cell, and that cell goes on to become a viable organism, the altered genome is incorporated into that organism's genome and passed on to the next generation (becoming an 'endogenous retrovirus', or 'ERV'). Estimates vary, but up to 5% of the human genome is understood to be made up of ERVs (it is thought that some artefacts that are considered to be ERVs did not actually originate with retroviruses, but we needn't complicate matters here). ERVs can be used to identify hereditary relationships between different species. For example, if the first common ancestor of all mammals was infected with a certain ERV, we can expect all mammals to have that same ERV. If the common ancestor of mice and rats had been infected with another ERV, all mice and rats should have that ERV as well as the first one. If the common ancestor of apes and humans had a certain ERV, all apes and humans should have the first one and the one from their common ancestor, butnot the one shared by mice and rats. Using ERVs then, we can trace out a complex family tree which exactly matches the evolutionary history of modern organisms that have already been established by other means (fossils, gene sequencing, body plans, geography, etc.).
There are copious examples of genetic evidence for evolution, but another particularly striking example involves the human "Chromosome 2". All the great apes have 24 pairs of chromosomes (which hold the DNA), but humans have 23 pairs. If humans evolved from a common ancestor with apes, we would expect to see evidence of two of those pairs of chromosomes merging into a single pair. At each end of each chromosome is a telomere - telomeres do not normally appear in the middle of a chromosome. In the middle of each chromosome is a centromere - there is normally only one centromere per chromosome. So a chromosome typically looks something like this: tt--------cc--------tt (where tt is the telomere, and cc is the centromere). Chromosome 2 in humans contains two telomeres in the middle of the chromosme, and a centromere in each half: tt----cc----tttt----cc----tt - indicating that this chromosome must be the result of the merging of two other chromsomes - which of course correspond exactly with the disparity between the chromosomes of great apes and humans. The gene sequences on these chromosomes in chimps and humans can be matched up (in fact they are almost identical), and prove beyond reasonable doubt that apes and humans share a common ancestor.
Atavisms and comparative embryology: Another strong indicator of evolution is the presence of vestigial traits in the genetic code, in embryos during their development, and sometimes even in fully developed creatures (where an ancestral feature is present in a creature, such as hind limbs on a whale, it is known as an 'atavism'). All vertebrates (including fish, reptiles, birds, and humans) share the same characteristics during early embryonic development - they all start out with the same type of skin, 'gill arches' (not gills, but the scaffold on which gills develop in fish) and a tail. As development progresses, the different groups of animals diverge along their evolutionary path - an early human embryo shares characteristics with early fish embryos, early reptile embryos, and other mammal embryos. Embryonic development is like a miniature evolutionary history played out in the womb.
Humans have the genetic information needed to grow a tail. The tail is very much in evidence during the embryonic stage and although it is usually re-absorbed during later development, some people are in fact born with a tail (not all cases of humans with appendages are true tails, but some are - there are documented cases of tails containing vertebrae and even muscles allowing the tail to be moved at will). Dolphin embryos have the 'buds' of hind limbs (even though dolphins don't have any form of hind limb). Chickens have the genes for teeth (and these genes can be artificially 'switched on' to hatch a chick with teeth). Attempts are underway right now to create a 'chickenosaurus'. By switching on the teeth genes, suppressing the gene that re-absorbs the long tail, and trying to locate the gene for keeping the fingers separate (chicken embryos have fingers which become fused into a wing during development), scientists are attempting to create a more dinosaur-like creature from the genetic material present in a chicken's DNA. They can only do this because the genes are already there - leftovers from the chicken's dinosaur ancestors. This is not something you would expect to see if creatures were special creations, but is exactly what is predicted by evolutionary theory.
The fossil record: The amount of fossil evidence in support of evolution is staggering. One of the interesting things about fossils is that it would be very easy to prove evolution wrong simply by finding a fossil in the 'wrong' layer of rock. Even when a layer of rock cannot be accurately dated, we can certainly deduce the order in which the layers formed - newer rocks being laid down on top of older layers. Thus, the depth or layer of rock that a fossil appears in indicates where it should fit in the evolutionary tree. If evolution is true, the deeper we dig, the more primitive forms should dominate - it would be impossible to find a fossil of a flower in the Paleozoic layer for example. This is not the case with special creation - species would not have to be created in any particular order, and even if the creator decided to make organisms more complex as time went on, their fossil placement still would not have to fit perfectly with the evolutionary tree, but again we find that without exception, the fossils we find are ones that fit exactly with the evolutionary model.
Despite creationist protestations about 'missing links', there are lots of examples of transitional forms in the fossil record. Huge numbers of fossils have been found in China and the US in recent years which provide quite a detailed account of the evolution of birds - from sparse display feathers to non-flight plumage to gliding dinosaurs to powered flight (in fact, birds are classified as avian dinosaurs today). The evolution of humans, whales, horses and other modern species are also very well documented in the fossil record. Don't take creationists' word for it that transitional fossils are 'missing' - they aren't. Look them up!
Also note that every time a new fossil is found, it creates an extra gap - where there was previously one gap between two species, on finding an intermediate form, you now have two gaps between those species! So we should expect that the number of gaps between fossils will increase as more ancient species are discovered (fossilization is rare enough that we will never find every link between every organism that ever lived), but the existence of gaps in the record is entirely expected and does no harm to the theory of evolution.
The above points are actually an extract from a new free e-book I am about to publish, about my reasons for leaving the JWs. I would appreciate any feedback!