You’ve probably heard of the liger and the tigon, offspring of a lion and a tiger together. But what about tiguars, tigards, liguars, lipards, jaggers, jaglions, jagupards, leogers, leopons, and leguars?
It is unusual but not unheard of for separate mammal species to interbreed. The mule, of course, is a well-known combination of a horse and a donkey. Wolves, coyotes, and dogs can combine to create wolfdogs, coydogs, and coywolves. Sheep and goats can actually rarely interbreed, despite being not only different species but in different genera:
Other hybrids include camels and llamas (camas), dolphins and false killer whales (wholphins), and grizzly bears plus polar bears (grolars or pizzleys?):
The kings and queens of mammal interbreeding have to be the different big cat species: lions, tigers, jaguars, and leopards. They encounter each other quite rarely in the wild, but various zoo encounters have led to a very wide range of unusual hybrids.
Lions + tigers = ligers (male lion, female tiger) and tigons (female lion, male tiger)
Tigers + jaguars = tiguars (male lion, female jaguar) and jaggers (female lion, male jaguar)
Lions + jaguars = liguars (male lion, female jaguar) and jaglions (female lion, male jaguar)
Lions + leopards = lipards (male lion, female leopard) and leopons (female lion, male leopard)
Tigers + leopards = tigards (male tiger, female leopard) and leogers (female tiger, male leopard)
Leopards + jaguars = leguars (male leopard, female jaguar) and jagupards (female leopard, male jaguar)
Some of these hybrids are only hypothetical – no-one has seen a verified living (as opposed to stillborn) jagger or tigard, for example. But various zoos have produced actual leopons, lipards, jaglions, liguars, and leguars. Most often they bear the markings of one or both species, with one parent’s head shape and – sometimes – the other parent’s body shape. Like mules, they are often infertile.
[Thanks to Gareth E.]
The Generalist Academy 
It’s explained in Dr Tatiana’s Sex Guide to All Creation why lions, living in prides, have pressure from the male to have few large children but from the female to have many small, whereas tigers, who are solitary, work the opposite way. (I’ve forgotten the reason, alas, but recommend the book highly.) Ligers then end up with both parents looking for huge babies, and wow, do they ever get them.