If you are touched by a kappa, you will have no way to escape. You will be under his control. So here are two ways to escape. First, Kappa has an obsession with cucumbers that they consider better than human flesh (which is good for you: p). Just feed him cucumber and he'll thank you by sparing your life. In the Edo era, it was customary for people to throw in the river cucumber with their name or their children's names written on it as well as their dates of birth. This way the family thought they were spared for at least one year because they had fed the yokai. If you don't have a cucumber on hand, you would still have the second method: greet like a Japanese. Indeed, being of rare politeness, when you greet him he will greet you in return. It is at this exact time that you will have to run as far as possible. Because of the salute, the small hole on the top of his head will be empty. Without his water, he will lose all his powers and be paralyzed.
Also “records” of violent moments, where they will attack cows and horses for no reason, and will hurt women.
But once you can gain respect and friendship from a Kappa, they will be loyal to you forever, granting any tasks you wish for them to do.
Might be the inspiration for the 2007 animation film, Kappa no Coo to no natsuyasumi.
In current media, Kappas are used as motifs of mockery and childlikeness.
Kappa have undergone a bit of Disneyfication that bowdlerised out their gruesome aggression and strict need for water in their bowl. It is a necessity of and to their immense popularity, courtesy of which they pop up in a lot of Japanese works for many different audiences. Even those works that aren't explicitly mythological like to throw in a kappa or two. While the kappa hasn't reached the same level of popularity elsewhere, Pop-Cultural Osmosis from anime means that Western works sometimes do feature one.