I would not just let it go. I don't believe in giving anything to anyone else's pet without permission, and I expect the same respect in return. You never know if a dog has specific health problems or what hassles you might cause another person if you do such things, so to me it is unacceptable behavior. Also, what if it turns out the neighbor has harmful intentions in the long run?

Some people are cruel enough to poison their neighbor's pets, among other things:
http://www.chicagobreakingnews.com/2009/09/man-accused-of-trying-to-poison-neighbors-dogs.html

Depending on how much interaction I've had with the neighbors and how friendly they appear to be, I would either say something directly to them as politely as possible or write a brief letter to them in order to have a record of exactly what I asked them to stop doing. If they absolutely refused to stop and kept trying to sneak food to any of my animals, I wouldn't be shy about involving animal control or the police.

That said, no one around me would be likely to get away with it in the first place, because I'm almost always out in the yard with my dogs when they are out.

Here's an informative page about what happens if your dog has been given rat poison and what to do about it:
http://petcare.suite101.com/article.cfm/how_to_tell_if_a_dog_has_eaten_rat_poison

Here's another page on prevention and treatment, which also includes some discussion of different plants and foods that may be harmful to pets:
http://www.americanhumane.org/protecting-animals/adoption-pet-care/safety/pets-and-poisons.html

Be safe, everyone!

http://www.boomspeed.com/saberdeen/BigDogSeesYou.jpg

The right thing to do is to speak to them. Table scraps are different than left overs, dogs should never have table scraps (that being things that people WILL NOT eat themselves).

Many table scraps are dangerous to pets, fat, bones, grease, etc. Gravy and salt and so forth, that may be on the scraps can contribute to health problems in the dog and this should be pointed out.

They probably mean well, so instead buy them a bag of dog treats with the provision that they only give your dog 2-3 a day.

I'd just ask them not to do it ... if you don't give the request a confrontational tone, I don't think they will be offended.

First, I can't imagine how it is acceptable to have your dog under the table while you are dining with your friends. Not only it is not polite, it is distracting and is a terrible habit for the dog. Even when your dining room is mixed with your living room, you can lock your dog to their doghouse or even your room.

But if I found myself in this situation, I'd ask them not to do it anymore kindly, and explain that it can make the dog sick. If they continue to do it, I'll just take my dog away from the dining room and apologizing to have the dog in the dining room at first place.