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Short answer: most solid, non-hazardous junk and construction debris can. Anything that can leak, burn, explode, or poison can't: liquid paint, fuel, batteries, propane, chemicals, and appliances with refrigerant. Tires, mattresses, and electronics fall in between and depend on your state and hauler.
Rules come from three places: federal law (such as the EPA refrigerant rule), your state's landfill bans, and your hauler's contract with the landfill. Every item page lists its sources. When rules differ, the strictest one applies, so always ask your hauler for their prohibited-items list before you load.
Related: what can you put in a dumpster (guide) · landfills and drop-off sites · debris weight calculator