Is it really necessary to keep old appliance boxes?

The only reason to keep small appliance (mixers, blenders, toasters, etc.) boxes would be for packing if they were planning to move to another home. Other than that, the old boxes should be recycled. Unused camping gear could be sold in a yard sale so someone else could get some use of them instead of letting things rot away and a basement or storage shed. Perhaps you can convince your parents about clutter having the potential risk for fire or as nesting places for critters. Good luck.