Nearly everything a Round Rock house, garage, or yard produces can leave on a junk truck. The exceptions are few, specific, and worth knowing before pickup day — so here is the full inventory, honestly sorted.
Yes, broadly

Furniture in any condition, mattresses, appliances, electronics, exercise equipment, grills, patio sets, playscapes, fencing, disassembled sheds, yard waste, remodel debris, and the undifferentiated cubic yards every attic and closet system eventually yields. Condition decides routing (donation versus disposal), never whether it hauls.
Yes, with conditions
Refrigerators, freezers, and window units: certified refrigerant recovery first — routine, but a real line item. Hot tubs and pianos: disassembly-and-crew jobs, quoted from photos. Mowers and grills: fuel drained, propane detached. Screens and TVs: hauled, then routed to e-waste rather than landfill.
No, firmly
Liquid paint, gasoline, oil, solvents, and pool chemicals; asbestos-suspect material (test pre-1980 flooring and insulation before demo); medical sharps; ammunition. These belong to household-hazardous-waste collections and specialty channels, and no legitimate hauler improvises around them.
The universal tiebreaker
Unsure about an item? Photograph it at booking. Every dispatcher has ruled on a thousand leaning sheds, full freezers, and mystery drums — you will have a yes, a no, or a price in minutes, and pickup day will contain no surprises at all.
One rule to remember
Solid and non-hazardous hauls; anything that pours, fumes, or needs a license has its own channel — usually the county's household-hazardous-waste collection, usually free.
For everything in between, the booking photo is the tiebreaker: a yes, a no, or a price in minutes, and a pickup day with zero surprises.