Framing, drywall, shingles, siding, flooring, cabinets, windows, and ordinary cleanout junk all go in without fuss. Virginia sets the limits, and so does the facility that takes your load.
Virginia makes it unlawful to put a used lead acid battery into mixed municipal solid waste at all. The rule covers the route, not just the landfill, so a car or boat battery in a roll-off container breaks it as surely as one in a curbside cart. They go to a retailer, a wholesaler, or an authorized recycling point instead.
Tires are the other common catch. Virginia requires tires to be split, cut, or shredded before they go into a landfill, which is why they are declared at booking and handled separately rather than tossed in with the rest.
There is also a rule about what a demolition-only landfill may legally accept. Under state regulation those sites may take construction, demolition, debris, and land-clearing waste, split tires, and white goods, and nothing else. Mixing household trash into a demolition load can therefore get it redirected.
Hazardous waste, liquids, paint, solvents, and fuel stay out of a standard container everywhere. Household hazardous waste and electronics have their own drop-off days at the transfer station. If one item has you unsure, ask your account manager before it goes over the side.