An interesting idea is doing the rounds in the press at the moment. Around 13,000 years ago (in the Late Pleistocene period) there were a number of extinctions of large mammals in North America. A team from Cornell University proposes to reintroduce large mammals into southwestern ranches. They may start with Asian asses (don’t search Google with that unless you’re open minded ;-)) and Przewalski’s horse, the latter being the only extant species of wild horse and an endangered species. Horses were prevalent in the USA before the last ice age.
Later on in the experiment, they propose Cheetahs and Elephants as other species to introduce into large private parks. North America could once again be home to a number of animals which originally lived in the wild there. One fear I have is that this kind of artificial introduction of species into an ecosystem could have unknown side effects on the food chain; most articles I have read present the positive side in several paragraphs and then just add “the risks are not trivial” at the end. To give a truly balanced argument one might think about the example of Australia where many pests were introduced either voluntarily or accidentally. The whole continent is now home to many feral animals (domesticated animals that have become established in the wild) and rodents which cause many problems.