Let's say you've got a sheep and a goat (and a bioengineering lab) and want to have a little fun. Why not make a geep? Geeps are created in the lab by effectively mashing up fertilized embryos from sheep and goats, then implanting the result into sheep or goat mothers. The resulting animal isn't a hybrid, it's a chimera: an animal with two genetically distinct sets of cells inside it.
Thus a geep looks like a sort of frankenpet, with patches of its body exhibiting furry goatlike features and others looking like a wooly sheep. Wikipedia has a picture of this cute (?) little fellow:
But here's where it gets nerdy. Apparently some scientists (including Dr. Gary B. Anderson of UC Davis, who provided the above photo) don't approve of the term "geep," preferring the much less catchy "sheep goat hybrid." But the term "geep" has a foothold in the popular imagination, appearing as early as 1984 in a Time Magazine article and in a recent Daily Mail article -- although the latter was referring to an entirely different kind of animal.
The Daily Mail article linked above describes something that isn't a chimera -- it's a rare natural hybrid between a goat and a sheep, created the old-fashioned way (see coverage by our friends Neatorama). Goats have 60 chromosomes while sheep have 54 chromosomes; one hybrid from Botswana, known as The Toast of Botswana, had 57 chromosomes and was infertile. For more on these true hybrids, including a picture of the Botswana animal, check out this BBC article or Wikipedia.
For more on the creation of geeps, run, don't walk, to listen to Radiolab show #404: So-Called Life. (It covers genetically engineered animals of various kinds, but includes some great geep material towards the end.)
Lastly, be careful not to use the term "shoat" when describing these animals. Although it looks like a handy conflation of "sheep" and "goat," shoat is actually a term for a baby pig. Thanks, Wikipedia!