The many homologies between living organisms offer powerful evidence for evolution in and of themselves. However, there is another way of looking at the data that ties the various homologies together into an even more powerful form of evidence: the hierarchy of life. There are only a couple of ways in which all life on earth could be related and once you visualize them, it becomes clear that only one pattern is supported by all the physical evidence: evolutionary theory.
What Evolution Predicts
If common descent actually happened, the general theory of evolution predicts that:
1. All of life should be groupable into a hierarchical, nested tree of organisms which shows the closeness of their relationships to each other; and
2. No matter what metric you use to develop the tree, you should get very similar trees.
To recognize what a powerful prediction this is, you have to consider that, outside of evolutionary theory, there is no reason for species to fit into nice nested trees at all. In fact, you should expect that they would not form such trees because many of the characteristics they posses would be based on independent variables. You should expect to find contradictions that would prevent you from organizing life into any sort of hierarchical, nested tree which has, by definition, a "root" or common origin point.
Comparing Trees of Life
This is easier to see by clicking on the image above, comparing the different ways in which life on earth might be related. The vertical direction is time and the horizontal is change of characteristics of life forms.
(a) Common descent;
(b) Transformationism. Note that species can change significantly but that they have independent starting points. No common ancestry.;
(c), (d) and (e) Creationism. (d) and (e) are creationist explanations for extinctions and/or appearance of new species over time such as are shown in the fossil record. Note that while the creationist paradigms are drawn as stright lines some minor variation might be allowed (i.e. within "kinds")
Hierarchy of Life
With a small number of attributes you might be able to make some subtrees just by chance even if life forms arose independently. However, it would be incredibly improbable for you to form a consistent set of trees for all life forms from different, essentially independent characteristics. Given the number of species to group and the number of possible characteristics, there are an enormous number of possible trees that could be formed. Many times the number of atoms we would expect in the universe.
The improbability of forming fairly consistent hierarchies from characteristics of lifeforms which arose independently makes the creationist claims about the improbability of abiogenesis or the spontaneous origin of the universe seem incredibly likely by comparison. It also makes the claims rather hypocritical, given how often they try to use statistics and probability to argue against evolution — though their claims about abiogenesis and cosmic origins are largely flawed or irrelevant as well. If we just consider large groupings of organisms, for example the 29 major taxa, there are over 1036 possible ways to arrange the classes into a tree.
Convergence of Independent Evidence
Possibly the most compelling evidence for common descent is that, not only do life forms fall into nice hierarchies based on just about any set of characteristics you would like to look at, but every set of characteristics you choose to group by yields trees that are very similar! The same basic phylogenetic tree can be arrived at by independently looking at similarities of anatomy, proteins, DNA, or other biochemical characteristics.
The only rational explanation for this is if all life originated from a common ancestor — we should expect life forms to fall into nested trees of similarity if all life arose from a common ancestor. What this means is that the fact that life forms do form these sorts of consistent trees is an amazing verified prediction of the general theory of evolution and a powerful piece of evidence that it is correct. As more genetic codes are decoded and more comparisons are made, they continue to fall into place. With the amount of work on decoding the genomes of various organisms that is going on today, new pieces of evidence for evolution are arriving regularly. The general theory of evolution has withstood the test of all the data.
