What are common ways to say goodbye in Japanese for different situations?
さようなら - Sayonara
But really, sayonara isn't used in that many situations. For example, you should use it with your teachers if you're a student leaving a school for the day. It's a formal greeting in this way.
But in other situations it can have the understanding that this is the last time you plan to see someone. It's a very permanent feeling way to say goodbye.
So while it's the most well known way to say goodbye outside of Japan, it's really not used much within Japan. It's a heavy word that is only used in certain situations.