The main rule of thumb for homeowners to follow when there is an easement on the property line is to avoid building anything, including fences, on said easements. Building a fence on an easement is risky, because the property owner may be ordered to take it down, or find it destroyed by a public utility that has easement access to the property.
The dominating rule regarding easement agreements in real estate titles is that the easement holder has rights to use portions of a property without the property owner's permission. A neighbor with easement rights to access part of a yard can rightfully demand a dividing fence be removed. Utility companies with easement rights can also tear down a fence to perform maintenance repairs. Utility easements can be above or below ground, and these are usually electrical power lines, gas lines and telephone lines.
A utility company might choose to rebuild a destroyed fence, but property owners should speak with a company representative to find out how it handles fences obstructing its path. Instead of a fence, property owners can create a natural barrier using bushes. Any type of shallow-rooted shrubbery planted on an easement is preferable to a permanent structure such as a fence, or big obstacle such as a tree.