I'm sure everyone here remembers the un-PC ditty for the resistor color codes...
Whats wrong with "Big Beautiful Roses Occupy Your Garden But Violets Grow Wild"...
I've seen it just memorized in order of the rainbow. For example, we start with BLACK, then BROWN as it is a mix between black/red, and then RED is next. So first 3 colors are BLACK, BROWN, RED. Then you have basically the rainbow starting with RED.... ORANGE, YELLOW, GREEN, BLUE, VIOLET. Then from violet you need to get to white on the end, so you have GREY in-between the violet and white, because if you mix violet and white, you get a light purple/greyish color (ok, it's a stretch but that's the only one off). That's easier to me than memorizing a sentence, to be honest.
As far as the multipliers go, it is just 10 to the power of the color's number. So BLACK being a 0, so 10 power 0 is 1x. BROWN is 1, so 10 power 1 is 10x, and so on through to BLUE which is 6, or 10 power 6 is 1,000,000x. After that, you memorize gold 0.1 and silver 0.01, and the tolerances BROWN (1%) RED (2%) GOLD (5%) SILVER (10%) (also same order as all the other digits). If no band then 20% tolerance.
Not sure if this is harder than the mnemonic.