Most household and construction debris is fine to load. The limits come from Wyoming's disposal rules and from the City landfill that takes your container.
Wyoming requires that all solid waste go to facilities approved by both the state and the local government, and Laramie's landfill is the approved site for this area. It runs separate drop-off areas for tires, batteries, refrigerators, metal, glass, and recycling, and it charges for some of those items by the piece. Refrigeration units carry their own fee, and tires are billed one at a time, so keep them out of a mixed load.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos can't go in a standard dumpster. The landfill treats asbestos and petroleum-soaked soil as special handling, so those need their own arrangements.
Residents can drop off household electronics at the landfill for free, which is an easy way to get old TVs and computers out of your container.
When you're not sure about an item, ask your account manager before loading it.