Standard goodbyes

3
再见 zàijiàn goodbye (standard) (literally "see again")
拜拜 bài bài bye-bye (borrowed from English, very common)
bài bye (short form, among friends)

Depending on when you'll meet again

5
回头见 huítóu jiàn see you later (when you'll see them later today)
一会儿见 yīhuìr jiàn see you in a moment (in a few minutes)
明天见 míngtiān jiàn see you tomorrow (meeting tomorrow)
下次见 xiàcì jiàn see you next time (no specific date)
后会有期 hòuhuì yǒu qī we'll meet again someday (more literary, for a long separation)

Formal or leaving formulas

4
我先走了 wǒ xiān zǒu le I'm heading off first (when leaving a meeting before others)
我先告辞了 wǒ xiān gàocí le I take my leave (formal, professional)
失陪了 shīpéi le excuse me for leaving (very polite, formal)
保重 bǎozhòng take care (warm, for a long separation)