It can be difficult to find the right opening sentence for an email. Below are some common expressions for starting business emails. Also see these business email closings.

Making an Announcement

Please be advised that…(formal)
Please be aware that…(formal)
Please note that…(neutral)
We are pleased to announce…(for good news)
We are proud to announce…(for good news)
Effective immediately…
As of (date)…
Due to recent events…
As you know…(announcing something people are aware of)
We regret to announce…(for bad news)

Note that we can also start an announcement with an infinitive.
To address our issues with…
To better serve our customers…

Making a Request

I am writing to request…(formal)
I am writing in reference to…(formal)
I am writing to inquire about…(formal — requesting information)
I would appreciate it if you could…
(formal request)
I was wondering if you could…
(formal request)
Do you think you might be able…? 
(formal request)
I am interested in finding out more about…(neutral — requesting information)

I would like to know if…(neutral — requesting information)

Do you think you could…? (neutral)
Would you please…? 
(neutral)
Could you please send…? 
(neutral)
Could you please…? (neutral)
Can you please…? (neutral)

Following up on a Conversation

As per our discussion…(formal)
Per our discussion…(formal)
In reference to our earlier conversation…(formal)

This is to confirm that…(confirming something the writer stated during a conversation)
As we discussed on (date/day)…(neutral-formal)
Regarding our conversation on (date/day)…(neutral-formal)
As I said on (date/day)…(informal)
Like I said on (date/day)…(informal)

Apologizing

Please accept our apologies for…(formal)
We would like to apologize for…(formal)
We sincerely apologize for…(formal)
I am deeply sorry for…(formal)
I’m sorry, but…(informal, used for minor transgressions — ex. I’m sorry, but I have to reschedule the meeting)
I’m afraid that…(used for minor transgressions or softening bad news)

Extending an Invitation

We would like to cordially invite you to…(formal)
You are cordially invited to attend…(formal)
We would be delighted if you joined us…(formal)
We would like to invite you to…(neutral)
You are invited to attend…(neutral)

Note that for invitations to a well-known business contact, less formal language is acceptable.
Would you like to go…?
Any chance you’d like to…?
I’d like to invite you to…

Congratulating Someone

Congratulations on your…
Congratulations on being…
I was pleased to hear about…
I was happy to hear about…

Reminding Someone

Just a friendly reminder that…
Just a quick note to remind you about…
Just a brief reminder that…
Have you had a chance to…? (gently reminding someone to finish a task)
Just checking on the status of…(gently reminding someone to finish a task)

Delivering Bad News

We are sorry to inform you…
We regret to inform you…
We regret to announce…

Note that we can also use expressions with due toafter, and despite to communicate bad news.
Due to (reason) we are unable to…
After consulting with…,
After evaluating…

Despite our best efforts,…

Responding after a Delay

Please excuse the delay in responding to your last email…(formal)
I apologize for the delayed response. (formal)
Sorry for taking so long to get back to you. (neutral-informal)

Requesting Payment

Our records show…
According to our records…
This is a reminder that…
Note that if multiple emails are needed, the tone typically gets progressively more direct.

Responding to a Complaint

Thanks for letting us know about…
Thank you for informing us about…
Thank you for sharing your experience with…
Thank you for taking the time to write to us…
Thank you for your email…

Note that many experts recommend starting these responses by thanking the customer. The actual apology usually comes later in the email. Some common expressions we use to apologize in response to a complaint include:
We’re sorry for any frustration this may have caused.
We’re sorry for any inconvenience this may have caused.
We sincerely apologize for…

Acknowledgement

Thank you for your prompt reply…(formal)
Thanks for getting back to me so quickly…(neutral)
Thank you for the detailed response…(formal)
Thank you for your order of…(neutral)
Thank you for completing…(neutral)
This is to confirm that we have received…(neutral)
Thank you for your email…(neutral)