The best is the 9's table, how all the digits add up to 9. My mom's an elementary teacher and there's always a few third graders who figure that out on their own and love it.
I think the usual 10 * n - n makes more sense and is much easier to remember.
So if X is divisible by 9, then the sum of the digits (mod 9) is zero.
Same works for 3 (x is div by 3 iff the sum of the digits id divisible by 3). And 11 gets an /alternating/ sum of the digits, since 10 is -1 mod 11...