I remember a few numbers from before i got a cell phone--my parents' landline, my grandma's landline, my high school friend's number (we're still friends and he still has the same number, but there's no good reason to actually still remember it)
Lately I'm working on memorizing a couple emergency numbers in case i here arrested at a protest without my phone
The advice I heard was to write it on your arm. I thought I was being overly paranoid until I saw someone else there with a marked up arm. I also found out that a Sharpie marker will still fade if you get sweaty.