Saber-toothed tigers are also an excellent example of the consequences of human over-hunting. From the current issue of Conservation magazine:

More than 25,000 years ago, one megafaunal species--we humans--began to spread rapidly around the globe and in the process helped to wipe out about half of all land mammals weighing more than 44 kilograms (97 pounds). "More than 101 genera perished," Anthony Barnosky, an ecologist at University of California, Berkeley, reported in a 2008 study in Proceedings of the National Academy of Sciences (PNAS). Among the victims were whole groups of mammoths, mastodons, saber-toothed tigers, giant ground sloths, and big beavers. Many vanished in just a 4,000-year span that ended about 11,000 years ago. By then, Australia had lost roughly 88 percent of its big mammal groups, South America 83 percent, and North America 72 percent. Africa did better during what is now called the Quaternary Megafauna Extinction (QME), losing about one-fifth of its big species, while Eurasia lost one-third.

Exactly what caused the QME has been the subject of long and fierce debate, but most explanations finger some combination of two ingredients: human hunters and rapid climate change. It doesn't take a PhD to realize that big mammals roaming across vast territories were obvious, attractive targets for hungry hunters seeking the biggest bang for their buck. It takes a little math, however, to see just how quickly unconstrained "overkill" can eliminate a species, such as the elephant, that reproduces slowly (as big mammals tend to). Sometimes, it can take just a few human generations. Toss hunting pressure into an environment already changing rapidly due to events such as human-set fires and yo-yo climate shifts, and it's no surprise that the stress "robbed global ecosystems of the biggest animals on Earth," Barnosky told a packed lecture hall a few years ago.

By his count, just 183 large-mammal species survived the catastrophe, often in dramatically reduced numbers. And their days are numbered unless we learn from the past, he argues in his provocative and eye-opening PNAS paper. The fundamental problem, he says, is that we're literally taking the lion's share of Earth's resources--and the shares needed by all other megafauna, too--for ourselves. The QME represented "a dramatic change in the way energy flowed through the global ecosystem," he writes. Before the extinction, there was easily enough "biomass"--the fundamental source of energy created when plants convert the sun's rays to edible tissue--to support some 350 big-mammal species. As hungry Homo sapiens spread, however, "energy began to flow toward a single megafauna species: humans." In addition to simply eating other big animals, we grabbed vast swaths of their habitat to grow crops and raise cows, goats, and sheep. In essence, Barnosky says, "we replaced the extinct megafauna with us and in the process lost a bunch of species that are never coming back because we now have grabbed their biomass."

This article also adds an interesting twist to the discussion of fossil fuels (and human population growth and...):
 

One puzzle, however, remains: Why have just a handful of big mammals actually gone extinct in the past few thousand years, even as human and livestock populations skyrocketed? One answer is that some, such as the American bison, are actually "dead species walking"--reduced to small, unsustainable population sizes or marginal habitat fragments and unable to survive without human help. Another answer, believes Barnosky, is that we temporarily took pressure off wild ecosystems when we discovered fossil fuels and then used that energy to supercharge our ability to feed and shelter ourselves. But that era appears to be closing, he notes, as humans press in on the few remaining habitats still dominated by nonhuman megafauna. It's no coincidence, he says, that human impacts now threaten some 90 species of large mammals, including 40 percent of those in Africa, a continent that made it through the QME largely unscathed. And with a rapidly warming climate taking hold, he says, the present is beginning to look eerily like the past: "Growing human populations and climate change? Beginning to sound familiar?"