Most debris from a remodel or cleanout can go in your container. New York's disposal rules and the transfer station that takes your load set the limits.
The New York State Department of Environmental Conservation says consumers must recycle computers, computer accessories, TVs, and small electronics instead of throwing them out. The state also bans burying waste tires in landfills. Keep both out of your dumpster.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos aren't allowed in a standard dumpster either. Propane tanks and other gas cylinders, motor oil, and fluorescent bulbs need their own disposal route, too.
For Village residents, the Department of Public Works takes TVs and computers at its yard, since they aren't picked up at the curb. If you're not sure about an item, ask your account manager before you load it.