There are many reasons to be an annoying neighbor. Perhaps you've got neighbors that aren't exactly your cup of tea. You can get them to move instead of trying to get along. By being an annoying neighbor you'll soon see a "For Sale" sign in their yard. Or maybe you just like being the most annoying neighbor because it's fun or because you're a cranky, old curmudgeon.
Measure your property line exactly. If your neighbor has a fence or any structure that even trespasses on your property by a millimeter, make them move it. That goes for tree branches that hang over your fence, as well. If in doubt, sue them in court to make sure they have nothing on your property or in the public domain restricted area. Be prepared to pay court costs if you're wrong.
File numerous complaints with your home owner's association alleging that your neighbor isn't following deed restrictions. This could be as simple as not mowing and edging, leaving their garbage cans outside after the allotted time allowance or playing music too loud. Join the HOA's monitoring group and you'll even have the power to send the out-of-compliance letters yourself.
Let the grass grow long and the weeds prosper. And when you do mow, let your grass clippings blow onto the neighbors sidewalk and driveway. This annoying habit works best if you're in good with the HOA so you won't get non-compliance letters.
Undress in front of your open window every night. This really doesn't work unless your neighbors are priggish, have young children, or if your body is, so to speak, in need of some repair work.
Paint your house a bright lime green or some other garish color. Make sure trim and paint do not match. This is a somewhat expensive way to be annoying, but over time your paint choice will drive your neighbor up the wall. Beware, it may upset your entire neighborhood so check your deed restrictions first.
Breed dogs on your property. This could be as simple as always having a female dog in heat in the backyard so that all the neighborhood dogs hang around barking, or you could even start a business with numerous dogs on site all the time. Feel free to let the little monsters dig under the neighbor's fence to play with their pets.
Randomly leave pieces of garbage out that can blow into your neighbor's yard. After dark, of course, when you won't be seen. It's best to find smelly garbage that might attract loose dogs, making it even more annoying since the dog will probably shred the garbage into even smaller pieces and might leave little "doggy gifts" for your neighbor to step in.
Encourage your children to play in front of the neighbor's house. Let the little tykes be as loud as they want. If your neighbor isn't kid-friendly, ask them to babysit often or just drop by with your kids for a friendly visit, say you forgot a pot on the stove, then don't come back for an hour.