No one wants to pull their boxes from storage and find their valuables crushed or broken. Bubble wrap is important to protect breakables. Wrap precious items in it to prevent bumps, dings, scrapes and cracks.
Fill boxes completely full. If you have extra space in the box, crumpled newspaper is a simple way to fill the box completely and keep it from being crushed, protecting your stored items from damage.
It sounds simple, but writing "Fragile" clearly on all boxes containing fragile items should help your movers or friends giving you a hand with your move to know which boxes to handle with particular care.
Finally, if you'll be storing electronics, please be mindful of the temperature! Cold weather can damage electronics, erase hard drives, and ruin television sets. If you must store electronics during cold weather, wrap them in some blankets for extra protection.