Most renovation and cleanout debris can go in your dumpster. New York State's rules set the main limits.
The New York State Department of Environmental Conservation says that since January 1, 2015, certain electronics can't be thrown away in landfills, waste-to-energy plants, or the trash. That covers computers, laptops, tablets, monitors, printers, game consoles, DVD players, and TVs larger than 4 inches.
The same agency bans burying waste tires in landfills, so tires need to go to a tire recycler.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos can't go in a standard dumpster either. Propane tanks and other pressurized cylinders stay out as well.
For appliances, the City's Bureau of Sanitation runs metal pickups by appointment from April through September. Refrigerators must have the Freon removed first. Call 914-665-2465 to schedule.
If you're unsure about an item, ask your account manager before it goes in the container.