It is not common in nature. A working definition of "species" is two genetically distinct populations of animals that are closely related enough that their sperm and ova are capable of crossbreeding, yet differently enough that they don't regard each other as potential mates. In my day we defined them as being of the same "genus," in fact that was the definition of "genus," but apparently the definition has changed and I still have no idea what it is now.
In many closely related species of warm-blooded animals (mammals and birds) whose territories overlap so they run into each other, the big issue is the courtship ritual. Male birds, for example, have elaborate mating dances and if they don't do it right, the female will not be aroused and interested. Tigers scratch the hell out of each other with their claws and lions really really hate that, so lions and tigers don't mate.
There are exceptions when a population becomes "distressed" and mates are hard to find. An animal's instinct to propagate its genes overrides its instinct to mate with one of its own kind. Wolves were practically eradicated in many parts of North America, so they started mating with coyotes. The hybrid offspring from eastern Canada are migrating south into the northeastern U.S. and mingling with the native coyotes. As a result we've got hybrid coyotes here in Maryland that are almost twice as big as the ones back home in California, fifty-pound monsters that are rather frightening. I think our deer problem has been solved.
Man's disturbance of nature causes hybridization in other ways. The area surrounding human settlements has become a new kind of habitat, teeming with the perfectly good food we throw away and the rodents and bugs it attracts. This is ideal territory for scavengers and hunters of small prey, except for the fact that most animals are not comfortable around our noisy, energetic habitations and are reluctant to feed so close to us. Naturally there are always a few individuals who decide that we're not that scary, and the easy life provided by the bounty of food on the fringes of our settlements is well worth the risk of learning to live around us.
It stands to reason that those curious, adventurous individuals will be the same ones who have no taboos about inter-species dating. I've been told by aviculturists that they saw riotously colored hybrid macaws raiding the dumpsters behind restaurants in Latin America, or begging for food like crows.
The rose-breasted grosbeak was indigenous to the eastern USA, and the black-headed grosbeak to the west. Their ranges were separated by the lovely dense rain forest that used to grow along the Mississippi River. Since the forest was cleared and replaced by farms, both species of grosbeak were attracted by the crops--they particularly love the fruit in orchards. They're both pretty in-your-face little birds and hybrid mating wasn't much of an emotional challenge for them. The first reports I've read of hybrid grosbeaks on the banks of the Mississippi were from the 1960s. Today we have them at our feeders in California. They crossed the Rockies in forty years.
Hybridization of plants is similarly an effect of civilization. Cross-pollination can't be prevented, but it's certain that the hybrid seedling won't be as well adapted to the conditions in the region as either parent species. However, when we come along and mess up the landscape by building a road across it, we change the conditions. Botanists say that stands of hybrid plants are fairly common sights along roadways.