I'm a disaster prep junkie - not a doomsday prepper but a practical junkie. Family disaster prep can seem overwhelming but if you take things a little at a time it's doable.
One of the best resources I have found is the Red Cross Disaster Preparation Calendar - you can find it on this link: Disaster Preparation Calendar
I'm also a tech junkie so to ensure you have electronic copies of things you will need, this link give great suggestions on what to put on a flash drive: Be Ready in a Flash.
Think about your pets - have an emergency kit for your pets and a carrier to keep them in if disaster strikes - they will be scared and may instinctively want to flee.
You can store items in a 55 gallon container (depending on the size of your family) which takes up very little space.
Put a sleeping bag, water, protein bars (or other edibles) and a change of clothes in the trunk of your car.
Keep a "shelter-in-place" kit at your work area - mine has a flashlight, trail mix, water, waterproof tarp, hand sanitizer, medications, toothbrush, toothpaste, wet wipes and a few other things.
Keep some cash on you. If a disaster strikes you may not have access to ATMs and banks may not be accessible.
These are just a few things that can help families (and individuals) be better prepared if the unthinkable happens. Here in Oregon, we are overdue for a 9.0+ subduction zone earthquake and when it happens I know I may have the tools for my family to survive.
Update: I forgot to add first aid kits and items to purify water! Thank you to webranding for the reminder!