I’m getting conflicting reports about this, but is incest common in the animal kingdom? If so, does it happen across the board, or is it limited to certain animals? How about domesticated vs. undomesticated?
Deja Vu for some of your questions.
There are a lot of good answers in that thread. Basically, for most of our primate relatives, either the males or the females leave the troop at puberty in order to avoid incest. Incest occurs more often in captive populations where the primates are not as free to move around.
Also in primates, males are more likely to commit incest than females, presumably because fathering an infant is less costly than mothering an infant. The males were responsible for the approaches in all of the incest stories I’ve read about for chimpanzees and often the females will refuse to mate with their male relatives. Another example of how this difference can be seen is in lesbian relationships developed by Japanese macaques. Although incestuous pairings have been observed in heterosexual relationships, they have never been observed in lesbian relationships despite the large numbers of such relationships observed. Here is a study which posits that there is “strong tendency of females to avoid incest and suggest[s] that males are primarily responsible for the reported exceptions to incest avoidance.” Of course, this is in primates and the results cannot be interpreted to be true for all mammals.
I’ve heard that many animals instinctively avoid mating with any animal that smells too similar to themselves.
A lot of animals have systems that prevent or at least reduce the probability of mating with a close relative, and they can include scent recognition and/or behaviors like males leaving the area once they reach reproductive age.
But for your second question, it’s definitely limited to certain animals. Invertebrates, especially broadcast spawners, don’t appear to have good ways to prevent incest. Corals, for example, just spew their sperm and eggs into the water hoping that they will meet. Barnacles pretty much have to mate with whoever is within reach (although their reach is legendary 
.) In the case of these animals, planktonic dispersion means they’re unlikely to be right next to a relative, but you never know. There could be subtle biochemical mechanisms of preventing inbreeding in these invertebrates, but they would be hard to find.