Quite a few, besides the obvious benefit of knowing the history of ourself as a species; knowing who we are and why we got here. To give just a few examples: Evolutionary studies shed light on what traits makes us human, what distinguishes us from (and make us similar to) other species. The evolution of such traits helps us understand why we act as we do, and helps us see that we are not fundamentally different from the rest of the living planet. We also better understand what causes things to go wrong, what causes diseases and why and when these develop. Perhaps equally important, it helps us understand our interactions with our environments through our evolutionary past, why and how these interactions took place, and therefore how we have ended up so dangerously close to a global environmental catastophe.
The evolution occurs as a response to the changes in the environment, the genotypes not suitable for the new environment will die or be sterile and not contribute to the next generation, but the suitable genotypes have high fertility and viability and will be the normal type in the new environment.
The human actions change rapidly the environment conditions, so we expected this actions will be a force directed the evolution.
In addition to the importance of better understanding past human behaviors, relationships with different and changing environments, there is a budding field of evolutionary medicine. Biological anthropologists, some medical anthropologists, and a few research and practicing physicians are working to recognize how some of the recent and very rapid changes in human lifeways present challenges to our bodies that evolved under very different conditions until the advent of agriculture ~10,000 years ago, the more recent industrial revolution, and the accelerating changes of the 20th & 21st centuries. Look at the publications of Daniel Lieberman related to questions of lower back pain, flat feet, dental crowding, and potential dietary problems contributing to obesity and diabetes. Evolutionary psychology is another interesting paradigm, although I am less sanguine about some of the methods of these studies that use large samples of modern college students to assert discovery of anciently evolved propensities (my pet peeve would be "beauty" studies that suggest what college students find attractive goes back into our deeper evolutionary past and is relevant to addressing the very different conditions of mating in traditional societies vs. dating among young people who are not immediately going to start having children or needing to hunt and gather for their livelihood). Evolutionary medicine also holds many promising ways to use more informed understanding of population variations (rather than "racial" categorization) to improve diagnoses and outcomes in medical research and treatment.
The study provides an insight to better understanding of the extinctions or evolutionary successes of the hominids at different time levels interacting and adapting with the changing environments through our evolutionary past. It is a constant struggle for existence. But, we moderns have very little dependence on our natural environment, and governed more by our artificial city environments we have created for us such that new bio-cultural adaptations would govern our present and future course of life about which we are uncertain and directionless. There is a big gap between our modern and traditional cultural values and biological adaptations, and old selection pressures may not be going to help us much to determine our future course of evolution. Due to our exploding population, we are under constant threat of polluted environment leading to new biological and pathological struggle within us. The humans are now dangerous killers than the Paleolithic hunters or the historical warriors.
Evolutionary genetics studies provide robust evidence that most if not all Homo sapiens sapiens populations on the planet, including nation-states are a big mix of haplogroups and archaic inserts from Neanderthals and Denisovans. So in terms of nation-state politics there are no 'pure' peoples or, in obsolete terminology 'races'. For so-called Western nations, speakers of Indo-European languages, there is no ethnic purity. Currently the US, Europe, etc are confronting a rise in neo-Nazi ideologues. They still believe Germany, or some sort of Aryan nation, must be kept pure. mtDNA genetics, for example, shows that of all the nations of Europe Germany has one of the highest rates of haplogroup diversity. In that sense it is the most racially 'impure' country in Europe. Similarly in a country like Brazil, the Spanish descendent white political elite thought itself pure, but genetic studies showed every sample analyzed for that group had a percentage of Native American and/or African genetics. No ethnic purity anywhere on the planet except perhaps a few indigenous hunter-gatherer tribes with 100% of a single haplogroup. Such knowledge in simplified form should be taught as part of every school curriculum. Diversity is who we are. And as the philosopher Nietzsche once said, in part against the antisemites in Germany, history proves that only cultures that have racial mixing are creative.
James makes a very important point linking scientific research with views in popular culture. The average % of nucleotide diversity between any 2 humans randomly compared across the earth is 0.1%. Of that proportion of differences, research indicates that the proportional variance among population samples from Africa, Asia and Europe also is very low. Approximately 85-90% is found in all of these groups and only 10-15% variation exists between them (of that 0.1% of DNA that does vary between individuals). There is absolutely no scientific support for ideas that modern human populations are discrete grourps without significant genetic similarities to every other human on earth (see attached file Jorde & Wooding 2004, among many others)
The best thing about studying evolution is that it severs stupid religious dogma and even more stupid and destructive racist ideology from actual reality.
We are all Homo sapiens and the sooner we accept that we are all one species that is a product of evolution and not created out of dirt, the better.
How many wars have been fought to show that Homo sapiens in one culture is better than another Homo sapiens from another culture?
And how many wars have been fought to demonstrate that an invisible god of one Homo sapiens culture is superior to another invisible god of another Homo sapiens culture?