Ordinary construction and cleanout debris is fine: framing, drywall, plaster, brick, roofing, flooring, cabinets, doors, carpet, furniture and household junk.
Hazardous material is not. Paint, solvents, thinners, fuels, motor oil, pesticides and pool chemicals all stay out, as do asbestos, free liquids and pressurized cylinders. Village houses from the plaster and lath era are prime candidates for asbestos in old floor tile and pipe lagging, so test before demolition rather than during it.
Electronics have a separate route here. The Village states plainly on its solid waste program page that residents may no longer throw televisions, video recorders and game consoles into their regular garbage, and it runs a free drop-off for them instead.
Burning is not an alternative. The Village code makes it unlawful for anyone owning or controlling a lot in the Village to burn garbage or similar matter on it.
Tires, appliances and anything holding refrigerant need to be mentioned at booking so they can be handled separately. Where an item is borderline, your account manager will settle it in one call.