Can a hero exist without a villian?

No, a hero is one that is admired for their triumphs over something bad. Whether the bad is a disease, a person...etc this had to be overcome. Without going into the philisophical details of good and bad, There must be something that is generally viewed as bad in order for a hero to arise.

To rationalize this concept you must think of a hero, any hero you can think of. Then think of why they are a hero. If the answer is try overcame an evil or (bad) there the villain. If they have a gift, such as a superhero, there must be an opposing force. Spiderman could save a cat from a tree or fighting doctor octopus there is always an enemy or villain.