The other way is to study how living things have gone out of existence, that is, the destiny of species. And not to take anything away from evolution, but the problem of extinction may be the more worthy one. After all, the origin of our species is a fact, and while it's satisfying to learn more about it we can live perfectly well not knowing. But it would be worth learning how to keep our species from becoming extinct.
Extinctions come in different sizes and have different causes. Individual species die out all the time, throughout the geological record. Since most species are local, so are the causes—slow changes in the land erased their habitat, or a competing species pushed them into oblivion. This is not likely for the human species.
Sometimes a larger number of species is snuffed out at once—that is, over a span of time that might be a thousand years, or even a million. The causes might be changes in climate, like an ice age, or a drop in sea level that erases the shallow seas where many specialized creatures live. Earth scientists tend to seek gradual causes for these episodes of heightened extinctions. The breakup of continents, or major changes in ocean chemistry or the atmosphere's composition, are the usual suspects.
On the whole, though, life withstands these trials and expands. It's generally accepted that living things today come in more species, and exist in more habitats, than in the distant past. When it comes to species, origination wins out over extinction. (The Fossil Record 2 database at the University of Bristol is a good way to explore the numbers.)
But there are a handful of very severe, mass extinctions that beg to be explained. Consider the events at the end of the Ordovician Period, some 440 million years ago. Nearly half of the brachiopods and bryozoans perished. The trilobites were devastated. In all about 100 families of marine invertebrates went extinct. (There was no life on land at this time.) Even worse was the mass extinction that ended the Permian Period, and the Paleozoic Era of which it is a part. Whatever happened then, about 250 million years ago, wiped out more than 95 percent of all species. Our species would have pretty dim prospects, too.
Maybe you have an idea what did it, if you've been watching TV or visiting museums for the last decade—an asteroid impact, like the one that killed the dinosaurs! Well, there was indeed a great impact event at the end of the Cretaceous 65 million years ago, when the last of the dinosaurs and many other groups of organisms went extinct. The question is settled in places like Hollywood movies (consider Disney's "Dinosaur"), popular museums (typical is "Blast from the Past" at the National Museum of Natural History), and the abstract arguments of physicists and astronomers.
But other lines of evidence exist, and many of them point a different way. Fossil evidence and geochemical evidence show that mass extinctions are mostly due to factors on Earth. Even the Cretaceous impact happened during a period of enormous volcanic eruptions, a thousand times greater than any in recorded history. The eruptions, along with changes in sea level and continental alignments, were staggering the dinosaurs and other life forms of the time. The impact came during a Cretaceous mass extinction that was already in progress.
On the whole, mass extinctions during the last 300 million years, where dating methods are fairly precise, aren't correlated with impacts. In general, a better case can be made for volcanism. So-called Large Igneous Provinces or LIPs occur in the record near a persuasively large number of mass extinctions, including the Cretaceous. As you read the sources in my Extinctions list, you'll see that when it comes to mass extinctions, most careful observers leave the door open for traditional geologic factors.
PS: Not that impacts are unimportant. Before Archean times, 3.8 billion years ago, life may have arisen on Earth more than once. That is, life may have suffered total extinction from impacts during that time, known as the late heavy bombardment.