Debi's suggestion is the best thing to try first, although you really don't want to commit to an apology on terms that you are in any way admitting that your dogs are doing the incessant barking. You'd be better served by expressing your regret that the neighborhood dogs' barking is so disturbing to your neighbors. In the meantime, you need to be gathering evidence to defend your dogs.
Have you thought about documenting the times that dogs are heard barking by tape recording and keeping a written journal of the day and time and where your dogs are at the time, possibly backed up by a time/date stamped videotape or photo?
The really infuriating part of this is that much of the outcome is going to depend on what kind of dogs you have and what kind of dogs the others have. If you have a large dog and they have a smaller dog, or if you have a Rottie and they have a Lab (for example), you're probably going to get the blame. Another factor is going to be which of you carries the most influence.
Back yourself up with evidence - perhaps - and this is gross - bag a couple of "samples" left on your neighbor's yard and a couple of the same from your dogs in your yard and show them the difference in size, color, etc., although if you can demonstrate this with photos or videotape it would probably be much appreciated. Our system of laws requires that the plaintiff (your neighbors) prove their allegations. Demand that they offer proof that it is always your dogs. That's impossible, especially since when one dog in a neighborhood barks, the others join in. That doesn't guarantee your neighborhood association will play by those rules, though. If you have some good evidence on your side and your neighborhood association still goes against you, have an attorney - one with a very creative mind - contact them with the possibility of a suit filed against them in court; try to enlist any animal advocacy groups in your area on your side, maybe even get them to join you in the suit. After all, there aren't any proscriptions about owning dogs in your subdivision, are there? And isn't it reasonable to expect that dogs are going to bark sometimes? Of course, this is a last resort, as most judges look at barking dog cases with all the enthusiasm of muddy dog looking at a bathtub.
Truthfully, if it were me, I'd be looking for a better neighborhood and putting my house on the market. But I really despise those kind of neo-Fascist environments anyway. The whole concept of making an investment in a home and then having everyone else be able to tell me what I can and can't do on my own property just strikes me as ludicrous. But I'll cut off my rant on personal freedoms and responsibility.
Good luck with this. I'm afraid you're going to need it. These people usually attack the person they think is the most vulnerable.
By the way, you'll get a chuckle out of this. I had a neighbor once who kept calling me at 3:00 a.m. or so in the morning to complain about my dog barking. My dog was asleep on my couch. He was snoring, but I doubt she could hear that! After telling her for the third time that he was in the house at night, I got smart and waited until about 5:00 a.m. (I knew she left for work at 8:00 so it didn't give her time to really get back to sleep) and called her and told her not to ever call again about my dog barking at night because he slept in the house on the couch and her phone calls were waking him up. That's the last I heard from her.
