If you don't know the name of the person you are writing to, start business emails with either of the following:
如果你不知道邮件是写给谁的,商务信函可以用下面任意一种方式开头:

Dear Sir,/Dear Madam,
尊敬的先生:/尊敬的女士:

Dear Madame, is wrong.
“亲爱的夫人”这种写法是错误的

If you don't know whether you’re writing to a man or a woman use:
如果你不知道是写给先生还是女士,可以写:

Dear Sir or Madam,
尊敬的先生或女士:

It is not usual to start an email To whom it may concern. This should be reserved for letters of reference or similar communications when the recipient is an unknown third party.
以“致相关人士”开头并不常见。这种用法一般用在推荐信或与其相似的交流中,收件人是不了解的第三方。

It is always better to use somebody's name if you know it. If it is the first time you are writing to someone, use either of the following:
如果知道对方姓名,邮件中写上总是好的。如果这是你第一次写信给某人,可以用下面任意一种方式开头:

For men: Dear Mr XXXX,
写给男士:尊敬的XXX先生

For women: Dear Ms XXXX,
写给女士:尊敬的XXX女士

Once you get to know someone, i.e. after exchanging one or two emails or if you meet them in person, it is usually OK to use their first name.
一旦你认识了对方,比如在往来一两封邮件或见过面以后,可以在邮件中称呼其名。

Use Dear Sirs, if you are writing to more than one person even if the group of people includes women.
如果你写邮件给两个或以上的人,即使这些人里有女士,请写“尊敬的先生们”。

Dear Ladies and Gentlemen, is wrong. "Ladies and Gentleman" is only used in formal speech.
"尊敬的女士们先生们”是错误的,这种用法只用在正式演讲中。

The word Dear may be omitted in less formal emails. Instead, you may just open with the person's first name/people’s first names.
“dear”在不是特别正式的邮件中可以省去。你可以直接以对方(个人或群组)的名字开头。

Here are some example opening sentences for emails:
下面有一些邮件开头的例句:

I hope you are well.
我希望你一切都好。

I hope you enjoyed your holiday and are finding it easy to settle back in to work.
我希望你已经好好享受假期并且很快重新投入工作。

Thank you very much for your email. I am glad to hear that you and your family are well.
非常谢谢您的邮件,我很高兴听到你和你的家人都很安康。

Thank you for your prompt reply.
感谢您的及时回复。

I apologize for not replying sooner, but I have been very busy these last few weeks.
很抱歉没能及早回信,但是过去几周实在太忙。

Thank you for getting in touch with us about XXXX. (Less formal, more friendly)
非常感谢您关于XXXX联系我们。(不是很正式,更友好)

Thank you for contacting us regarding XXXX. (More formal)
非常感谢您因关于XXXX的事接洽我们(更正式)

With reference to your email of [date], I would like to bring the following to your attention.
关于你(时间)寄来的邮件,我有几点想跟你说的。

As a follow-up to our phone call this morning, I would like summarise the key issues.
关于你早上的电话,我想总结下关键几点。

Phrases best avoided:
请最好避免:

I hope this email finds you well.
我希望这封邮件能被你看到。

Please be advised as follows.
请按照如下建议。

This email concerns…
这封邮件是关于……