Fairings were manufactured in Germany between 1890 and 1910. The adorable souvenirs were called Fairings because they were sold at town, city or state fairs. The most popular fairings were pigs because of the german correlation between pigs being lucky and also showing a sign of wealth. The second most popular fairing are bears because of the Teddy Bear craze going on in America modeled after Teddy Roosevelt.
They were mass produced and appeared in many of the same molds as the pigs. To get a better perspective I suggest you purchase the book "This little Piggy" at Amazon.com. Although the pricing is from 1992 it is a great reference.
There were other fairings made depicting lobsters, dogs, frogs and even devils. These figurines appear to be more rare. The themes are similar such as involving the figure with a basket, pin dish or shoe but these figurines in and of themselves are far and few between.
Here are some interesting links to other types of fairings: