I believe the most convincing evidence for evolution is the fossil record. The fact that animal fossils are layered from primitive to modern species from the bottom to the top of earth's rock layers is the most powerful proof that life evolved on earth. We can literally see the history of progression through the geologic column.
Creationists try to avoid this issue by saying that the fossil record is incomplete (true, but the general evolutionary pattern is clear), the fossil record is mixed up in places (true, but the general evolutionary pattern is still obvious), and that the fossil record is not really one of progression. This last claim--that rock layers do not actually record a progression of bacteria to modern life--is false.
One example of this deceptive claim occurs in the Answers In Genesis book "Refuting Evolution." On page 39, Jonathan Sarfati presents a diagram that he claims represents the history of life on earth:
Now the thing you must understand about this supposed graph of life is that creationists don't believe that one kind of animal evolves into another. They believe that groups of animals (like bears) can vary in form (like polar bears and black bears) but that these groups (or "kinds") are fixed and a bear could never evolve into some other kind animal.
So while Sarfati did not label the "trees" in his diagram, as a creationist he believes that each tree represents a family, or some other fixed group of animal like bears, dolphins, hawks and so on.
The problem with the creationist diagram then is that the trunks of all of these trees reach all the way to the ground. The diagram suggests that every major group of animals can be found down through every layer of the earth's fossil-bearing rocks--all the way back to the beginning.
Unfortunately for the creationist, this is absolutely not observed in the real world. Interestingly, another creationist book provides a more accurate and honest depiction of the fossil record. On page 95 of "Darwin's Enigma," creationist Luther Sunderland provides this diagram:
Note that I have rotated the diagram 90 degrees counter-clockwise so the vertical dimension represents the orientation of the rock layers (as if you are looking side-on with the edge of the earth). Sunderland's animal groups look like non-branching trees (he is trying to make the point that groups of animals don't evolve into other groups/kinds), but note that these tree trunks do not appear to all stretch back to the deepest layers of geologic column. The groups/kinds are not found all the way down through the geologic column.
This creationist diagram confirms the point that I can rarely get creationists to admit: that fossils in the earth's crust are ordered in an evolutionary pattern from simple organisms at the bottom to more complex and modern ones at the top. Look at the diagram: Bacteria and Algae appear first on earth. Then worms. Later, fish, amphibians, reptiles, birds and mammals.
If the diagram was more complete, we'd see that primitive birds (with teeth and short wings) appear before modern birds (eagles and robins). Jawless fish appear before jawed fish. And yes, monkeys and apes appear before humans in the fossil record.
The Answers in Genesis diagram is deceptive. It suggests that all kinds of life from dogs to dodos to dinosaurs appeared all at once at the beginning of time. The truth is just the opposite. Plant and animal fossils are arranged in an evolutionary sequence, and any theory of life on earth must explain this historical record.