When you leave home, the leaver says "ittekimasu" 行ってきますand the person staying says "itterashai"　いってらっしゃい.

If you want to be poetic, you could say さらば saraba, which is similar to the English farewell - and in its normal sense also used like that, as a last goodbye. E.g. さらば友よ！ saraba tomo yo! - Farewell, my friends!

Among friends you could also use the very informal あばよ abayo, but I would observe your friends first before using something like that. Some of my Japanese friends use it, and then I feel OK using it as well towards them. Its origin lies in the former: さらばよ sarabayo.

There is

さようなら。sayounara

じゃね。Ja-ne

and バイバイ。bai bai

That's all I know. o. o

In a work setting, there are some other ways that are cultural norms used in place of a typical goodbye.

1. お先に失礼します - osaki ni shitsurei shimasu - Excuse me for leaving before you. This is polite to say to co-workers because you are leaving before they have finished their work.
2. お疲れ様です（でした）- otsukare sama desu / deshita - You've got hard hard work left to do / You've worked hard. Has the understood meaning and sense of gratitude to someone working hard. So it's a polite expression to use with coworkers in many situations, but also for when you tell them goodbye in the evening.

Other things friends might say to each other:

またね！mata ne (much like see you later)

また遊ぼう！mata asobou (let's play [do something] together again)

じゃあ、また。jaa, mata (well then, later)

また明日！mata ashita (see you again tomorrow)

Not very interesting, but friends usually just say バイバイ (bye bye).

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.