Nearly everything a remodel produces can go straight in. The limits come from Illinois landfill bans and from what the receiving facility accepts.
The Illinois Environmental Protection Agency keeps several materials out of landfills by law. Landscape waste has been banned since 1990, lead acid vehicle batteries since the same year, appliances with their mercury switches, refrigerant, or PCB components still in place since 1994, and liquid used motor oil since 1996.
Fluorescent and high intensity lamps count as hazardous waste because of the mercury in them, and mercury-containing products have no landfill route at all. Paint, solvents, fuel, pesticides, and pool chemicals belong at a state household hazardous waste collection, which is free to Illinois residents.
The state does spell out what a container can take. General construction and demolition debris covers soil, plaster, glass, drywall, non-hazardous painted or treated wood, plumbing fixtures, electrical wiring, insulation, brick, wood products, roofing shingles, concrete, and roof coverings. Clean fill, meaning broken concrete without protruding bars, brick, rock, stone, reclaimed asphalt, dirt, and sand, is handled separately and is usually cheaper in its own load.
Holding an item you can't place? Run it past your account manager before it goes in.