Is there a "canon" of Zen Koans? There are lots of Koans on the internet, but I am not sure if there is some sort of process that a Koan must go through, or if there is some sort of list of Koans that are taught and that new ones are not added. 

Meaning, if a Koan is just made up on the spot by some random person, and the Koan is unrelated to the core principals of Zazen, I presume it wouldn't be taught by a Japanese Zen master. Which leads me to believe that there are some sort of "canon" of Koans.
Sure - the Blue Rock Collection, the Mumonkan, the Book of Serenity, etc.  We mostly stick to those because, frankly, they're freaking fantastic and have been leading people to enlightenment for over 1200 years.  Why reinvent the wheel?  Of course, just about every teacher will often make up a koan on the spot to help a student with a specific obstacle.  Some of these remain in circulation among some lineages, but they rarely (if ever) rise to the prominence of something collected in the afore mentioned texts.