Most remodeling and cleanout debris can go right in. The limits come from Illinois landfill bans and from the facilities that take your load.
The Illinois EPA's disposal guidance notes that yard waste has been banned from landfills since 1990 and used tires since 1994. Keep grass, leaves, and brush out of a mixed load, and take old tires back to a tire shop.
Electronics are off the list too. The Illinois EPA says state law bans landfilling TVs and computers, so pull those out for an electronics recycler.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos can't go in a standard dumpster either. Mention appliances when you book, since some need special handling first.
Dolton adds a few house rules for curbside trash. Yard waste has to go out in paper bags, never plastic, and nothing can be dumped in the alleys.
If you aren't sure about an item, ask your account manager before it goes in.