One thing that I don't recall ever seeing mentioned here whenever a post about "memorization" comes up is exactly what one means by that. Rote memorization, like how we were forced to memorize multiplication tables in grade school? Or the playing-without-paper thing that many musicians, especially professionals, do?
I'm going to address the latter, and I'll start by saying even though I've played a long time and have been around music and musicians my whole life - I can't do it! At least not very well
But I know plenty of others who can, and in my experience, musicians you see in the non-classical world who play without a cheat sheet aren't playing from "memory" per se - they're playing by ear, or a combination of ear and memory; particularly rhythm players. When you understand chord structure and chord progressions that way, it's kind of like speaking a language - you know what comes next and you don't have to look it up. Same goes for the instrumental playing that happens during solo breaks - they know the scales and they know what key they're in, so they know where to go.
Just wanted to put that out there for all of those who "can't" memorize, as I'm one of them - rote memorization has always come very, very slowly and with great difficulty for me. Once I understand the *why* of it, it gets easier, e.g. I can pretty much play a I-IV-V or I-vi-ii-V progression in the more common keys "from memory" (just don't ask me to do it in, say, E flat!). But as primarily an instrumental player, I've probably memorized fewer than a dozen songs beginning to end, and even when I play those I prefer to have my sheet music in front of me (combination of standard notation and tab preferred). I think of it this way: if you go to a classical performance, the players always have sheet music. If it's good enough for the L.A. Philharmonic, then hey - maybe there's something to it!
