Framing lumber, drywall, plaster, roofing, flooring, cabinets, and household junk all load normally. The refusals come from New York law and from what the receiving facility will take.
Electronics are the firmest rule. The New York State Department of Environmental Conservation runs a manufacturer-funded recycling program for computers, monitors, televisions, and peripherals, and consumers are expected to meet the state's disposal ban by recycling those devices rather than throwing them out.
Car batteries are next. The same agency states that it is illegal to put a spent lead-acid battery in the trash, and a retailer has to take up to two used batteries a month from any individual at no charge.
Hazardous waste, liquids, paint, solvents, fuel, motor oil, and asbestos stay out of every container. The City also excludes asbestos waste, tires, appliances, fluorescent lights, and fuel tanks from its own construction debris collection, which is a good guide to what a load should not contain.
Tires and appliances holding refrigerant usually carry a per-item charge rather than a weight charge. Mention them to your account manager at booking and the quote holds.