While there are always exceptions to the rule, America is a property rights nation, where a land owner has explicit control over what he does with his land. If he wants to build a fence, he can build it without anyone's permission, as long as it is on his land. A problem could arise if the planned fence construction is so massive or odd that it violates a city ordinance or in some way infringes upon the rights of others, even if it is located entirely on the owner's land.
An issue sometimes arises regarding a fence that was agreed upon at one time, but, years later, one side or the other decides he doesn't want it anymore. Such a situation may have the potential for a legal entanglement, although certain points of law have evolved in some areas to address this circumstance. One example is in Idaho, where "boundary by agreement" is in effect. The basic point is that if there is evidence both neighbors agreed on the fence's construction, such as by splitting material costs or labor, the fence becomes the legal boundary, which allows either owner to build whatever he wants on his side of the fence, no permission needed.
Adverse possession is another legal concept observed in Idaho, though it is difficult to fulfill adverse possession based on its legal definition. Under this concept, a person can claim ownership of the property of another by openly using it for a period of time with no rebuttal from the true owner. When the time period was set at five years, frequent claims of adverse possession arose, but since the Idaho law has been increased to 20 years, adverse possession is much less common.
Some local ordinances allow you to build a fence at the property line, though no part of it can encroach onto your neighbor's property without his permission. Before building a fence on the property line, try to get a written agreement, which should be recorded at the county recorder's office, that allows you to access the fence from your neighbor's side for repairs and maintenance. If you can't get an agreement in writing, build the fence far enough from the property line that you can mow and make repairs without leaving your yard.
While it might be preferable to seek the permission of a neighbor before building a fence, as long as you keep it on your property and do not violate any city or homeowners association (HOA) building restrictions, you should be within your rights to do so. Besides knowing the city ordinance requirements and restrictions, the important issue is to be aware of where your property boundary is and stay on your side of it with any fence construction.