Play loud music, such as Metallica, through very large, multiple speakers.  When they come over to complain, point to your hearing aids, and say this is the only way you can enjoy music anymore.

Explain that your religion requires you to love thy neighbor, and preferably convert them as well, therefore propose to knock on their door each week to discuss 'saving' them.  If you cannot do this with real conviction, hire Jehovah's Witnesses to do this for you.

When their dogs bark, fire paint balls at them.  No matter if you accidentally hit their deck.

Bake 'special brownies' and take them over when they have visitors.  Don't mention secret ingredient.

Have your toddler pick their flowers.  Replace them with offensive political signs, such as Ron Paul's.

Teach your dog to fetch their newspaper and bring it to you.

Never ever rake your leaves all year long.  Then just before spring, buy a leaf blower, and blast them all in their direction.  

Make sure to park your RV within the view of their front window.

While watching their animals during their yearly vacation, also take them to the groomer to be completely shaved.

When they start avoiding you, call the police and report that they might be missing.

Every time you see a 'crime stoppers' commercial, call the phone number and report suspicious activity.  Give their license plate numbers and physical description.

Get a blaring car alarm, and conviently forget how to turn it off at two a.m.

Buy a huge flashing neon sign that will glare into their bedroom window.

Keep running over to tell them to 'keep their eyes out for the snake' who got out of the cage again.