Standard construction and cleanout debris loads without trouble. Lumber, drywall, siding, shingles, flooring, cabinets, doors, windows, furniture, carpet and cardboard are all fine, and clean concrete, brick and block belong in the smallest unit.
What stays out is the hazardous list, and it is the same everywhere for good reason: paint, stains, solvents, thinners, fuel, motor oil, antifreeze, propane cylinders, pool chemicals, pesticides, asbestos-containing material, wet batteries and liquids of any kind. None of these can travel in a container and none can be buried at a landfill.
Tires come out as well. They are handled through a separate route rather than mixed into a construction load, and leaving them in a container usually means the whole load is refused or repriced at the gate.
Two more practical Mokena points. Appliances holding refrigerant, so refrigerators, freezers and air conditioning units, need the refrigerant recovered by a certified technician before disposal, which is a job to arrange rather than a decision to make on the day. And electronics are worth setting aside, because a sorted pile of old televisions and monitors is easier to place than the same items buried in a mixed container.
If an item is borderline, say a sealed drum, a half-full can of deck stain or a water heater, put it to your account manager before anything goes in.