Blue is my favorite color!  Is it yours?
I do like blue. I like blues with a greenish hue, like azure. But other blues like ultramarine are pretty, too.
How does the different shades of blue come about?
It lies between violet and green on the light spectrum, so the closer the color moves to one side or the other, the stronger that color will be.
Interesting.  Does the color have any significant meaning to any cultures?
In many cultures. For example, in China in the eighth century artists would use cobalt blue for fine blue and white porcelain.
I imagine those items are worth quite a bit now, right?
I'm sure the originals are worth a lot. Especially as decorating them was done by brush painting. Now stencilling is employed; either that or transfer-printing.
I figured that.  Isn't blue considered a royal color?
It could be considered a royal color in some cultures. The ancient Egyptians used lapis lazuli (the stone) to make jewellery and ornaments.