Is there any legal action that I can take?

I am only licensed to practice law in Ohio so my response is limited by that restriction.  That being said, my suggestion for you is to read the New York statute prohibiting littering.  By way of comparison, the Ohio statute prohibiting littering is found at Ohio Revised Code 3767.32 and provides as follows. (B) No person, without privilege to do so, shall knowingly deposit litter, or cause it to be deposited, in a litter receptacle located on any public property or on any private property not owned by the person unless one of the following applies: (1) The litter was generated or located on the property on which the litter receptacle is located; (2) The person is directed to do so by a public official as part of a litter collection drive; (3) The person is directed to do so by a person whom the person reasonably believes to have the privilege to use the litter receptacle; (4) The litter consists of any of the following: (a) The contents of a litter bag or container of a type and size customarily carried and used in a motor vehicle; (b) The contents of an ash tray of a type customarily installed or carried and used in a motor vehicle; (c) Beverage containers and food sacks, wrappings, and containers of a type and in an amount that reasonably may be expected to be generated during routine commuting or business or recreational travel by a motor vehicle; (d) Beverage containers, food sacks, wrappings, containers, and other materials of a type and in an amount that reasonably may be expected to be generated during a routine day by a person and deposited in a litter receptacle by a casual passerby. So, by a strict reading of this Ohio statute, a neighbor next door commits the criminal offense of littering in Ohio by placing his trash in your garbage can.  If New York law has a similar provision, and if your neighbor continues to ignore your demands to stop such actions, you could file a criminal complaint with your local police department. If that does not work, you could bring a civil court action against the neighbor for trespassing on your property.  At common law, a trespass occurs when one enters upon another person's property without permission.  You may want to check the New York statutes on trespass as well.  Good luck.