Talk to Your Neighbor
A lot of times, people won't really know how their pets behave when they are gone from the home. If a dog spends most of his time outside, your neighbors may have no idea of how he behaves. Talk to them nicely about the situation and explain whatever problems you are having with the pet. In an ideal scenario, they will agree to take care of matters and train or get rid of the dog.
Bonus Tip: Ask your neighbor for his number in case you need to contact him about his dog's behavior while he is away. If the dog is digging holes in the backyard or causing other damage that could cost your neighbor money, he will appreciate the heads up.
Try to Find the Cause of the Rowdiness
You may be able to calm the dog down next door just by figuring out why he is being rowdy in the first place. For instance, if the dog is upset because of a neighborhood cat you feed in your backyard, consider moving the food to the front so the dog can no longer see the other animal. If the dog appears to be upset because he is hungry, thirsty, hot, etc., point those problems out when you confront your neighbor. Chances are there is a reason for the dog's behavior that could eliminate the problem altogether.
Protect Your Property
If you know your neighbors won't do anything or you're not confident about their ability to take action in a timely manner, you can take matters into your own hands. Add bricks or cement around the base of the fence to prevent the dog from digging his way in. Add spikes to the top of the fence to prevent him from jumping over. Put up security cameras to capture any escapes on film, or record incidences when you notice them. This will help if you ever have to go to court. The more you can do to protect yourself, the better off you will be.
Use Proper Confrontation
If you get the urge to harm the dog next door, by all means control yourself. You need to avoid confrontation as much as possible so that you don't get bitten or injured by the dog. If you need to have someone take care of the situation, report the problem to the authorities. Either the police or animal control will come out to assess the scene. They may take the dog away, or they may issue the owners a citation. Either way, you'll get some sort of justice out of the ordeal.