Move heavy furniture away from beds, couches, chairs and any other place where people may sit or sleep. For some added security, secure those heavy pieces to the wall. Hardware stores and major home and garden centers sell earthquake-safety straps and fasteners. Secure the furniture directly to the wall studs. Fastening to wallboard alone does nothing to prevent a piece of furniture from falling.
If you live in areas such as California where earthquakes are frequent, never hang anything over your bed and don't hang decorative mirrors anywhere in the house. Instead, hang soft art such as unframed posters or rugs and tapestries.
It's the law in California that water heaters must be strapped to the wall. Strap your water heater to the wall if you live anywhere else that earthquakes might occur. Hardware stores and major home and garden centers sell these materials.
Keep the clutter picked up from the hallway and all other areas in the home that receive foot traffic. If the earthquake strikes at night, you'll most likely find yourself without electricity. Anything cluttering up the floor is a potential hazard as you feel your way through the dark.
Install child-safety latches on all your cupboards in the kitchen to prevent flying glass. Remove from open shelves all glassware, collectibles, pottery objects and anything that can become a deadly projectile during an earthquake.