If you are in the City of Wilmington you will need to get a permit fromt the city and if you are in a historic district additional rules may apply.
If you are in the County you do not need to obtain a building permit, however if you are planning a very tall fence I would check with the planning department ahead of time to be on the safe side.
Generally speaking, in a non HOA neighborhood, you should be able to build a backyard fence up to 6 feet without too much of a hassle and a smaller front yard fence if desired.
You should double check with your HOA, the City or the County as may be the case in your situation. The planning and building departments are there to help you with your questions and generally get back to you pretty quickly.
Good luck with your project.
Have a great day!
I serve on the architectural committee of our HOA and we require a drawing and complete specifications. But mostly it comes down to common since. As Ian said there are codes to ask about and as Mike asked, do you live in the city or the county?