Do plants and animals always have two parents?

NO, both plants and animals do not have always have two parents.

Animals - For eg: Snail does not want to take birth from two parents. And also some kind of fishes (if I'm not wrong clownfish is good example) the largest fish in group became female which is able to reproduce.

Plants - for eg: Binary fission is the best example for this. In this One parent cell divides in two daughter cells and the process goes on