Created I was, in 1841,
By someone with the name of an evil one,
He was a Belgian, living in Paris,
This man had to be very zealous.
Adolphe Sax invented the saxophone in 1841. Adolphe Sax's name has a resemblance to Adolf Hitler, an evil one indeed...
Fourteen of me, this young man made,
Some above A, but not quite B,
With some higher than D, but lower than E,
And some that are C, and three halves above D,
That's why my popularity's so easy to see.
Sax made 14 different types of saxes. Seven pitched in C and F (F is three half-steps above D, hence three halves above D), and seven pitched in Eb (That's E Flat for you non-musicians, which is above D and lower than E) and Bb (above A and not quite B).
Golden with lacquer, I usually am,
I sometimes am used to honor Uncle Sam.
Saxes are usually golden, and the covering is referred to a lacquer. Saxes are also used in Military bands, thus "honoring Uncle Sam"
Patented I was in 1846,
I'm the one who gives some their kicks,
I'm shaped like a J-with a hook on the end,
Most saxes are J shaped with a hook with the exception of the Soprano Sax. Many Jazz enthusiasts get their "kicks" or enjoyment from saxophone players.