If you are entering into a real estate transaction, always be sure to have the seller point out the corner stakes of the property lines. Sight along those lines to take a quick inventory of trees, fences, overhanging branches, or back yard sheds that may cross over the property lines. People who have just purchased will want to confirm their boundary lines to see if there are any encroachments. Or, if you've lived there a long time and are preparing to sell, you will want to avoid last minute problems by being an informed seller. If a fence is installed in the wrong place, which results in some of your property being on the other side of the offending fence, then this can delay or endanger a smooth transaction.
The best way to solve a problem like this is in an open and cooperative fashion with the neighbor. Good practice would be to do some research first by talking to the previous property owner, or the neighbor who owns the fence, or other neighbors. You will want to find out how long the encroachment has been there. You will want to confirm your boundary line if the property stakes cannot be found.
The concern is that a neighbor can claim adverse possession if the condition has existed for the required number of years for that state. Keep in mind that the operative word here is "Adverse". For a property owner who owned both parcels and then sold you one of them, on which there was a misplaced fence, there only became an "adverse" fence placement when you took ownership of your new parcel. That would be the date where the parties would look to start marking time for a future "adverse" claim. The time varies by state, but in Washington, the time frame is 10 years.
The adverse possession claim must be supported by several factors that validate it, namely the use must be exclusive, continuous, it must be open and notorious, and hostile. No permissions will have accompanied the use of the property, and the offending party must prove that he has used and maintained the property as his own. Adverse possession claims are settled in the courtroom, so avoiding costly legal proceedings is strongly advised.
If the neighbor is resistant to moving his fence, removing the hedge, etc., then you can adopt a license agreement to memorialize a temporary permission. This would desribe the situation with a legal description of the property and boundary line, and giving the neighbor the right to temporarily continue the offending use by permission. It states that the permission can be withdrawn at any time by notice, and further that there will be no property claims adverse to the owner by such continued use.
I have a license agreement drawn up by an attorney here in Washington. It must be signed and notarized, even recorded. Once this step is taken, then the rights of the property owner are protected, and when the time for the termination of the license comes, the fence must be removed by the agreed upon notice provision in the license agreement.
Trees can also be a problem, since their brances can be a nuisance should they fall and break your prized rhododendron or trellis. It is lawful for branches that overhang your property to be removed, but it is still a good idea to notify your neighbor to avoid a problematic situation. Tree roots can also be an offending problem in that they can harm a septic drainfield, or disturb blacktop and or retaining walls.
As a long time Seattle area practitioner of real estate, I have run into all kinds of these problems and am well versed to advise a homeowner as to best practices involving problems like these. If you are reading this article and this applies to you, get in touch with me. I am eager to help.