1. When something is too heavy or awkward to move
2. When something is too big to put in the alley or at the curb
3. If you don’t know how to dispose of it properly. Most haulers will not except hazardous waste (electronics, paint, cleaners, CFL light bulbs), but may accept other hard to dispose of items like mattresses.
4. You have more than a car full of stuff or more than you can physically carry out the door.
If you're able, why not have someone come and haul it all away; or rent a giant dumpster to fill and miraculously have taken away?