When I was a small child, in the days with no cell phones, my parents made me remember my address and two phone numbers; those of my house and a house nextdoor. Even if I had some troubles when I was out, I could connect with my family anyway.
The March 11 disaster last year got me to need a stronger "kizuna" (bond) between people, but since I got a cell phone, I've never kept any phone numbers in mind. I just don't have to do so as the phone records all. To my shame, I sometimes forget my own cell phone number.
Feeling horrified, I decided to put off the habit. I started writing down the numbers on the directory in my smart phone. My family members' cell phone numbers have just been memorized.