This style of iron fencing is known as bow and picket. It is a combination design constructed with a picket under an arched piece (the bow), connected by horizontal rails. The post is called a square or solid post. This particular design also features an urn-like finial and designs on the post. While many of the pickets are simple, this features a fleur de lis element.
Woven wire fencing was also used in the late 19th century and there were a number of intricate designs available. This one combines the wire fence with a pipe or “gas pipe” railing. An acorn caps the post.
Two different types of crosses decorate the top of the pipe rail.
This is also a bow and picket style, however, the post is called an open or scroll post.
This is a variation of a picket design, with a line post. This fence appeared to be more recent than the others.
The original purpose of fences in cemeteries was two-fold: protect the graves from cattle and define the family plots. As styles of cemeteries changed, and the desire for easier maintenance developed, fences were no longer in fashion, and were removed in some cases. Theft of grave fences, particularly in isolated rural areas, is a major problem. One can find them at any number of antique stores around the country, but the likelihood is high that if you purchase it, you are purchasing stolen property from a cemetery or grave site that has been vandalized.