The recent wide use of genetic and/or phylogenetic approaches has uncovered diverse examples of repeated evolution of adaptive traits including the multiple appearances of eyes, echolocation in bats and dolphins, pigmentation modifications in vertebrates, mimicry in butterflies for mutualistic interactions, convergence of some flower traits in plants, and multiple independent evolution of particular protein properties. -Pascal-Antoine Christin, et al; "Causes and evolutionary significance of genetic convergence," Trends in Genetics; Vol.26(9), pp. 400-405, 2010
Convergence is a deeply intriguing mystery, given how complex some of the structures are. Some scientists are skeptical that an undirected process like natural selection and mutation would have stumbled upon the same complex structure many different times. Advocates of neo-Darwinism, on the other hand, think convergent structures simply show that natural selection can produce functional innovations more than once. For other scientists, the phenomenon of convergence raises doubts about how significant homology really is as evidence for Common Descent. Convergence, by definition, affirms that similar structures do not necessarily point to common ancestry. Even neo-Darwinists acknowledge this. But if similar features can point to having a common ancestor--and to not having a common ancestor--how much does "homology" really tell us about the history of life? -Explore Evolution, p. 48
One beautiful example of convergent evolution is the octopus that has camera eyes very similar to human eyes. There appear to be many similar genes responsible for the similarities between human and octopus eye structures. Granted, the genetic similarities are not as extensive as one might think, but there do appear to be many identical genes, nonetheless. Humans and octopi are very unrelated in evolutionary terms. How did similar eyes evolve in both? It is almost as if eyes were designed to develop and form specific configurations.
In some cases, like with corals and humans, there are many genes that are the same between species, even though they are not considered to be closely related. In the case of "simple" corals, not only do they have as many genes as humans, they even have genes similar to humans for immunity. Supposedly simple sponges have genes similar to humans for making proteins that nerve cells use to communicate, even though they don't have nerves. Researchers currently don't know why sponges should need so many proteins. Now, what appear to be sponge embryos have been found as early as 600 Ma, which is around the same time as complex animals just barely started forming. The point of all this is that all animals are complex and share common, complex genes. This presents a problem for naturalistic evolution.
All of this clearly supports the thesis that complex genetic information was present originally in the earliest life, whether that was algae or something else. The information needed for complex features was created from the beginning by God. The evidence points that way, from the best I can tell. The fact that so many unrelated animals share so much genetic code and that convergent evolution is so common is excellent evidence in favor of this thesis. Naturalistic evolution doesn't easily explain the ubiquity of convergent evolution--or even how it should happen at all.
To top it all off, there are a good number of examples of features shared between all living animals, like the circadian rhythms related to the night-day cycle, DNA repair systems, and systemic immunity. In naturalistic evolution, why would this circadian rhythm become an essential feature of all living things? It doesn't seem to be a critical feature for algae or other "simple" living things. Also, the innate immune system, which has recently been shown to be highly complex and efficient, is shared by many kinds of animals, including simple life, like sponges and insects. Such complexity and conservation of genes shouldn't be found in nature if it was all just incidental. (If you don't believe me about these specific things, please go do some research, and I assure you these facts are true.)
Specific Example Supporting Thesis
A team led by UC Santa Cruz postdoctoral researcher Gill Bejerano used high-speed computers to compare the gene sequences of humans and animals...
They found that the chemical sequence of certain segments of DNA in specific vertebrates precisely matches some DNA segments in humans. In all, they identified almost 500 segments that were "completely unchanged" despite tens or hundreds of millions of years of evolution in animals as seemingly unrelated as mice and men. ...
It's hard to understand how the oldest of these DNA fragments -- some more than 400 million years old -- could have endured unchanged over such an incredible length of time, the scientists said. By comparison, the dinosaurs went extinct relatively recently, a mere 65 million years ago.
These DNA fragments "are now evolutionarily frozen. We don't know of a biomolecular mechanism that would explain them," said Professor David Haussler of UC Santa Cruz, a computational biologist who runs the lab where his postdoctoral colleague, Bejerano, did most of the work. ...
-http://www.sfgate.com/cgi-bin/article.cgi?f=/c/a/2004/05/08/GENES.TMP (emphasis mine)
The above quote is pretty telling. The reason they don't know a biomolecular mechanism that can explain all the identical DNA fragments among vertebrates is because they misunderstand how evolution works! The only way these fragments could remain unchanged is if evolution is more intelligent and isn't randomly changing genes. The evolutionary process obviously must be more precise and nonrandom and organized by design.