Doing It for the Art: The first reaction of the producers at hearing from the animators that they didn't know how to do the rope bridge fight was encouragement; that meant that nobody had done it before and from that challenge, one of animation's wildest action sequences was created.
Growing the Beard: Served as this for the Dreamworks Animation Studio. Following it's release and success, Dreamworks backed away from trying to duplicating the Shrek formula. Even the Shrek's next sequel and spinoff took more of a page from Kung Fu Panda's book.
What Could Have Been: In an early version of the original movie's script, Po was intended to be something of a Parody Sue, expecting the Furious Five to love him and adore him as much as he liked them. Apparently, Jack Black intervened because he realized how unlikeable this made the character, and urged the writers to change Po to being insecure and well aware of his own flaws.
The creators were going to make Mantis The Mole until character designer Nico Marlet gave him more of a playful look that played with the stereotype of a creepy praying mantis.
For the second movie, there was time in the plot where a female mantis was going to eat him.
Before Kung Fu Panda 2 was released, there was information that pointed out a different backstory for Lord Shen then from what was shown: Shen's parents were said to be ashamed of his albino coloring and poor health, so they left him in the care of their advisor, the Soothsayer, who raised him like her own. Traces of this can be seen as Shen is never outright cruel to the Soothsayer, such as how he releases her before the launch of his armada, meaning that he still respects her for showing him love. This is the backstory used in the novelization.
The Wolf Boss was originally going to be a crow, but the creators thought that would make him too similar to Shen.
The Wu Sisters were originally going to be minions of Tai Lung in the first movie, but were taken out to make Tai Lung seem like more of a badass. Their original designs also differ greatly from their current ones, including them looking completely identical and having a rather obnoxious Verbal Tic. See for yourself.