Few realize that the continuity of life, and not the fossil record, was Charles Darwin's first and most powerful argument for evolution.
Scientists and those creationists that are opposed to evolution—for not all creationists oppose evolution—approach their arguments differently. Scientists tend to look at the whole picture, developing their theories from the import of the evidence as a whole. Those who oppose evolution, on the other hand, tend to throw out one argument at a time, hoping to find something that evolution cannot explain, something that could not have evolved.
An example of the "big picture" approach is Charles Darwin's book, On the Origin of Species. Darwin begins On the Origin of Species by pointing out how difficult it is to differentiate between a species and subspecies (or variety).
In his day, the definition of a species (on a practical level) was a life form that was independently created by God. A subspecies, on the other hand, was understood to have descended from another life form. For example, in the case of dogs, they all probably descended from wolves, so by that definition, wolves would be a species and chihuahua a subspecies. (We don't use that definition anymore, so wolves and domestic dogs are different species.)
Darwin then points out how naturalists of his time couldn't agree on what was a species and what was a subspecies. The continuity of life was too great! Life forms are too closely related!
Then he started considering the rock pigeon, which has been bred into many forms of doves in England. If the rock pigeon could be bred by humans into so many forms and so various, what would stop creatures from continuing to diverge and diverge until the differences were much greater than those seen in subspecies? He then points out that if doves were found in the wild, he's sure that they would not only be considered several species, but even several genera (plural of genus).
He then started looking in nature for indications that such divergence has been going on continually, and he was able to find many intermediate forms that are still alive today. He spends the rest of the book arguing almost exclusively from living forms that pretty much every animal and plant alive can be shown to be descended from or related to some other living plant or animal—perfect continuity of life.
He's very good at that argument.
At the same time, Alfred Wallace was drawing similar conclusions about the continuity of life based on the geographical distribution of animals.
That was 150 years ago. As time has passed, scientists have found more and more evidence for what Darwin and Wallace were seeing. As more fossils have been discovered, scientistists are finding that fossils have the same progression and the same smooth geographical distribution as living animals.
For example, marsupial mammals are found almost exclusively in Australia. The only exceptions, both living and in fossil, are in South America, which was once joined to Australia. Marsupials are not randomly distributed around the world.
You will notice, too, similarities between animals and plants in India, Madagascar, and Africa, which also were all once joined. India does not have similar flora and fauna to Asia, but to Africa. Elephants are found only in Africa and India, for example. This is because India used to be joined to Africa. After its tectonic plate carried it to Asia, it slammed into the Asian continent, creating the Himalayas and forming a natural border between itself and the northern part of Asia. Thus, its animals and plants are related to African animals and plants, not Asian. Again, a smooth continuity of life that can be seen everywhere we look.
In the fossil record, we take note of facts such as finding fossils of ancient, giant sloths in South America, where modern sloths live; not on other continents. Such continutity of life is evident throughout the fossil record and in living things today. It is almost always easy to explain how living species got to where they are today from their ancestors in the past and living relatives.
Even more conclusively, since Darwin's time, we've discovered DNA! We now know that every living cell reads exactly the same code. Not only do all cells have DNA, but every living cell reads DNA exactly the same way.
In other words, DNA is like an alphabet forming a language, and every living cell speaks the same language. It is not like human language, where there are hundreds of languages and thousands of dialects. All cells speak and read the same DNA language.
That's why we can take human DNA, put it in yeast, and get yeast to produce human insulin that can then be injected into diabetics. Yeast reads the same DNA code as human cells. So do all plant and bacteria cells.
Everywhere science looks, they see continuity of life.
I use the word "assault" here, but I don't object to creationists questioning the continuity of life. Questioning is what science is all about! It's only the dishonest dealings with the answers that I object to.
Creationists tend to look for specifics. Creationists hunt around for one event here or one event there in which it's difficult for science to find the continuity of life.
For example, Michael Behe (who actually acknowledges most evolution) is well-known in Intelligent Design circles. His most famous argument is the flagellum found in some bactera. It's a little spinning tail that they use to move. (Very impressive little design.) This flagellum is made of 15 proteins, and he argued that if you take even one away, then the flagellum won't work.
He then concludes that such a structure could not have evolved. It must have been intelligently designed.
Notice how Darwin discusses general principles seen in life, finds thousands of examples, notices a consistent pattern, then says he thinks it's possible all of life evolved that way? Behe, on the other hand, is working with just one, arguing that science can't explain this one occurrence.
Yes, Michael Behe looks for many such inexplicable items, but he is not stepping back, looking at the continuity of life, and drawing a conclusion. Instead, he steps forward and puts a microscrope to individual items, demanding an explanation for every step along the way.
The problem with the Behe method, though, is that eventually science usually can explain such items. In the case of the flagellum, it turns out that another bacteria has a very similar structure, with only 7 or 8 of those proteins, and that bacteria uses the structure as a needle to inject poison in cells. It then uses the poisoned cell as food. (Explained further here.)
One other issue is that creationists win most debates when they only last one or two hours. The reason is that creationists bring up individual items that they think can't be explained, then the scientist spends all his time explaining the majority of them. Usually, though, there's one or two—or ten—that he's never heard of (often because they're completely fabricated by dishonest creationists, so they've never made it into scientific literature, or they've just been invented the day before).
In this way, the scientist looks bad. He looks like he's spending his whole time trying to explain impossible things and succeeding only occasionally.
That scientist never gets the chance to do what Darwin could do in a long book. He never gets to explain the massive evidence in nature that indicates the spread of life and the smooth continuity in time and geography of life as we know it.
I saw one debate, between Kent Hovind and Ben Waggoner, where Waggoner turned the tables on Hovind.
This is a long video, but worth watching! Waggoner's technique is wildly successful, but he never gains audience support. Below I have another debate where the evolutionist is not so successful, but he does warm the audience up excellently.
He began the debate by saying he'd read Hovind's web site, and he was convinced evolution was a lie. Then he sat down and didn't use his time. After Hovind was done speaking, Waggoner said, "I do have to ask some questions because there's things I don't understand. Please educate me."
Waggoner then began showing bits of evidence for evolution that there was no way Hovind could explain. At the end of the debate, it was Hovind who looked like he was explaining impossible things, and Waggoner clearly won the debate.
In this video, Shermer tries to stick to the continuity of life and not get stuck on Hovind's details. He was only partially successful, and he said afterward that he never wanted to do another creation vs. evolution debate.