important, vital

必要(ひつよう)	A casual word for necessary

大切(たいせつ)	Necessary and also important. Stronger and more emotional than 必要。 I can’t live without you!

重大(じゅうだい)	A serious or weighty matter. Unlike the others, 重大 can apply to bad things or problems.

重要(じゅうよう)	More business-like than the others. Today’s top priority.

大事(だいじ)	Similar to 重大. But it has the nuance of, ‘If you mess this important thing up, we’re all fucked.’ In other words, something is important because failure to do that thing will doom the whole project. As opposed to ‘trust is important in a relationship.’ – 大事 is something to be lost.