Do wild animals ever cross breed, even across species?

Aside from a few musicians that I have known:

There are many modern examples of hybridization in nature, some forced, some natural. Mules are bred by humans from horses and donkeys, are completely sterile, and represent an evolutionary dead-end. But there are other species-crossings that do just fine, such as offspring of the notoriously promiscuous oak tree species, which hybridize so often species-namers commonly joke about not being able to keep up.

Still, cross-species matings usually result in sickness or sterility, if the offspring get that far --many naturally abort. Hybrid offspring that are fertile but sick or weak will not be able to compete with the purer offspring of either parent in passing on their genes to future generations. As a result, many evolutionary biologists have thought hybridization to be evolutionarily unimportant.

http://www.sciencedaily.com/releases/2003/08/030808081854.htm

Interspecies breeding (sometimes called cross breeding1) is the act of creating offspring from two different species. It should not be confused with the chimera which involves more of a Frankenstein-type process of gene splicing, cell modification, implantation, and embryo modification. While the creation and study of hybrid plants has been ongoing for hundreds of years, this writeup deals with hybrid species created by cross breeding in the animal kingdom - specifically mammals, however the concepts themselves cross these borders.

Interspecies breeding is a very complex subject. Obviously it is not possible to mate any animal with any other animal to produce a strange new creature. If you've learned anything from South Park, you will know that "pig and elephant DNA just won't splice". It is commonly believed that for two species to be able to interbreed, they must have the same number of chromosomes. While this is true in most cases there are many exceptions. For example, a horse (64 chromosomes) and a zebra (44 chromosomes) can produce viable offspring. If the animals have a different number of chromosomes, the animal with the smaller number must be the male (e.g., a male zebra and a female horse could produce a foal, but a female zebra could not be impregnated by a male horse). What is most important is that the chromosomes that do match up are homologous. What determines this homology at the cellular level is beyond the scope of this writeup.

In general, cross bred animals are sterile. This is typically related to the fact that even if the chromosomes match up enough to create the offspring, there are still genetic problems that cause the hybrid to be unable to produce children. In cases where then animal can (medically) produce viable eggs or sperm; it again becomes a problem of matching chromosomes with some other species. This is not to say that no crossbred animal can mate, it is just rare.

Most cross breeding occurs between animals in the same Genus. There have been cases where offspring has been produced between animals in different genera but in the same family. However, this is uncommon, and has caused some scientists to question whether the classifications of these animals are correct in the current system.

http://everything2.org/index.pl?node_id=1528852

Hybridisation in the wild:

It is extremely rare for any wild animal to breed with one from another species.

For instance, in the wild the Grant's and Thompson's gazelle live together happily in mixed herds. The species are very alike and only experts are able to discern one from the other. Despite this there are no known instances of these gazelle interbreeding.

The domestic dog will mate indiscriminately with another breed, but wild dog breeds, including wolves, foxes and coyotes, mate only within their own species.
In the early 1900s, Indian natives regularly spoke of an animal they knew as the doglas. It was claimed to be a hybrid between the leopard and the tiger. Though there were some large leopards in the area with striping on their abdomens, it was never established that the native claim accounted for the source of this odd colouring.

Throughout Mexico and South America there is a widespread belief that natural hybrids occur between pumas and jaguars, but animal biologists have been unable to find evidence which would substantiate this.

All crosses between wild and domestic animals are automatically considered to be domesticated. This includes animals like the beefalo (American bison x domestic cattle), Zorses (zebra x horses), zonkeys (zebra x donkeys), the wolf dog, and the various small wild cat x domestic cat hybrids.

http://www.lairweb.org.nz/tiger/hybridisation.html