Ordinary building and household debris is fine. Georgia publishes no statewide list of banned materials, so the practical limits come from the receiving site and from common sense.
Hazardous waste, liquids, paint, solvents, fuel and asbestos stay out of every standard container, and tires, batteries, appliances and electronics all need their own route rather than a mixed load. Name them when you book and your account manager will arrange them.
The City's own recycling rules are a useful guide to what has no curbside home at all here, and therefore belongs in a container. McDonough's recycling cart refuses food and food containers, polystyrene foam, packing peanuts, loose bubble wrap, restroom and kitchen wastepaper, glass containers, glass panels, fluorescent bulbs, photographs and film, and discs and their cases. Fluorescent bulbs in particular should be set aside rather than dropped into a container with everything else.
On yard material the City caps bagged waste at fifty pounds a bag and only stacks limbs between one and four inches in diameter and up to eight feet long, so a real landscaping clearance is a container job rather than a curbside one.