I'm not very good at using microscopes. Maybe that's one of the reasons I'm a chemist, not a biologist. The first problem is getting my eye to line up with that pesky small hole. The second problem is finding the right level of focus. If I'm focused in too much or out too much I don't see anything in the microscope at all. When I finally hit that magic level, everything comes crystal clear and I feel like a veil has been removed.
The same thing happens when looking at how evolution works. There are different "levels" to the world, and what you see differs depending on which level you're focused on. If you're focused on the level of nucleotides and genes, not much appears repeatable. But if you move your focus up, to the level of organism and environment, repeatable parallels suddenly come into sharp focus.
A paper that just measured this is titled "The Effect of Selection Environment on the Probability of Parallel Evolution". Here's a quote:
"Briefly, we find that parallel evolution is very common at the highest level of biological organization we can study, fitness, and becomes less and less common as one descends down the hierarchy to phenotypes, genes, and nucleotides."
This paper repeated evolution of a bacterium through about 1000 generations 15 times, varying the type of sugar and the location of the sugar. The most interesting finding was that evolution was more parallel when three sugars were located in distinct places than when they were mixed throughout the environment. This suggests that evolution is more predictable if the environment is more varied (and therefore more "natural," like the real Earth is, with diverse nooks, crannies, and caves). As we learn more about the heterogeneity of the early Earth environment, it's worth keeping in mind that any such heterogeneity may have made evolution more predictable, not less.
Evolution does have a random component, especially at the lowest levels. But it becomes more ordered the higher you go, until when you look at all of Earth's history, in the context of the complex Earth environment, the result becomes more and more predictable. And always remember, if you can't see anything, try twisting that focus knob on the side of the microscope.