Most building and household debris loads with no trouble at all. The limits come from Texas rules and from what the receiving site will take.
Texas names a short list of things that may not be disposed of at any municipal solid waste facility. That list covers lead-acid batteries, do-it-yourself used motor oil, used oil filters, whole scrap tires, refrigerators and freezers and air conditioners and anything else holding a chlorinated fluorocarbon, liquid waste, regulated hazardous waste, materials containing PCBs, and radioactive material. None of it belongs in a roll-off.
Paint, solvents, fuel, pesticides and pool chemicals stay out as well, along with asbestos. Televisions and computer monitors are their own case. The state says they may count as hazardous waste when thrown away, and a business disposing of them has stricter duties than a household, so recycling is the route it prefers.
One useful piece of good news: clean soil, dirt, rock and sand used as fill to make land buildable is not treated as solid waste at all in Texas. Keeping that material clean and separate can save you money. If an item has you guessing, ask your account manager before it goes in the container.