General:
* Carton
* Shipping box
* Moving box
* Storage box
* Container
* Crate (for larger or heavier items)
* Case (for smaller or delicate items)
More specific:
* Cardboard box
* Corrugated box
* Shipping carton
* Packing crate
* Shipping container
* Moving crate
* Storage container
* Display box (for retail products)
Informal:
* Box
* Cardboard
Technical:
* Packaging
* Shipping packaging
The best word to use will depend on the specific situation and the type of box you're referring to.