My dad recorded himself, "3*3=9, 3*4=12, 3*5=15 ... " and made us listen to the tape every night before we went to bed. I'm not saying I enjoyed it, but I can still hear my dad saying them :-)
I think he had us listen to a couple of numbers each night. Maybe 1's and 2's one night, 3's and 4's the next, etc. It wasn't so bad, and we did learn them!
My oldest is about to begin Kindergarten, so this is all new to me, but I do teach college remedial math. I always tell my students that the more you are able to understand math, the less you have to memorize. But most of us need to memorize first and understand later. I wouldn't be afraid to do some memorization. These are basic facts that they need to know.