For reasons I don't understand, phone numbers stick in my head, sometimes for many years. My kids have learned that it is faster to ask me for phone numbers than to look them up, even in a short list like a cell-phone's. I still remember the phone number of my best friend in second grade, even though I haven't called it in years. When I pull something like that out of my brain, the kids are more appalled than impressed (kind of like remembering the Frito Bandito jingle). Just don't ask me to remember what someone said two weeks ago - that I probably can't do.
Different phone numbers take different techniques to memorize. If there is some kind of a pattern with the numbers, such as 582-2044, it's easy and I may memorize the number visually in just a few phone calls. Sometimes I can find relationships between the numbers; I can remember 587-7049 by 7x7+0=49. If there is a good speaking rhythm, as in 585-5775, I'll remember it verbally. Other numbers are easier to learn by the dialing pattern, especially if they form a nice triangle like 3493. Some I learn kinesthetically, by writing them (or drawing them on my arm with a fingernail, if all else fails) repeatedly. And then there are a few numbers that I simply have to learn through brute force, by repeating them over and over until I remember them.
The problem with this is that I don't always memorize whose number it is as well as I do the number - so when I want to call the dentist, I still have to look it up to find a number that I recognize immediately.