Why would you want to sue your neighbor? Well, first, think very carefully about it before you do it. These cases are emotional, expensive, and rarely give you a real good sense of relief in the end. At least that's my experience. The typical claims against neighbors are for what is called a private nuisance. You are entitled to the quiet use and enjoyment of your property. The law protects that right and if someone's unreasonable use of their property interferes with your "quiet use and enjoyment" of your property, you can sue for damages, or an injunction to stop them from doing whatever it is that annoys you. Connecticut law has long recognized that a landowner may not use his property in a manner which infringes on the rights of other landowners. Examples include loud noise, smells, or trespassing on your property (that's a different type of claim and can lead to criminal charges). To get a court-ordered injunction is not easy (we've done it) and requires proof of (1) a probability of success on the merits (you are probably going to win your case) (2) irreparable harm (money is not enough, you need the conduct to stop!) and (3) lack of an adequate remedy at law (basically the same thing, money is not a sufficient remedy). You also need to show that it's more fair for the court to enter the injunction than not to.
On to SLAPP. That's a relatively new law in Connecticut that I have been paying some attention to. You can read here and here for some background information. A recent Connecticut case involved a nuisance of sorts. One neighbor complained to the local zoning official about her neighbor that was allegedly repairing cars on their property which was in a residential zone. The complaining neighbor took pictures and video, and presented a complaint to the zoning official who issued a cease and desist order, which resulted in an enforcement proceeding against the owners that were allegedly violating the zoning regulations. The Town sought an injunction and got one through a stipulated judgment (meaning the parties agreed to certain things in favor of the Town for the most part).
Well, then the neighbors sued the complaining neighbor after the zoning proceeding, for (2) trespass, (3) slander, (4) negligent infliction of emotional distress, (5) intentional infliction of emotional distress, (6) harassment, and (7) injunctive relief. The other neighbor filed a special motion to dismiss under SLAPP, claiming she had a right to "petition" the government and that is why she was being sued. She won, had the case against her dismissed, and the plaintiff, the party who brought the lawsuit, was ordered to pay her $13,121.93 in attorney's fees because it was improbable the plaintiff was going to win their claims against the picture-taking neighbor.
What's the lesson? Do not wait to enforce your rights, but consider all the consequences. Here, if the neighbors had immediately sued once the other neighbor started taking pictures, or trespassing, and before she complained to the Town, they might not have had their case dismissed. I'm not saying you should knee-jerk file a lawsuit, but don't wait to become informed of your rights. Often, timing is everything.