How do you greet multiple recipients in an e-mail?

If you don't know the recipients' names, I refer you to the other answers. However, if you do know their names, then I will add that I would actually just write:

Dear John,
Dear Jack,

I have been using this formula for more than a decade. So far, nobody has complained. For me, this approach has quite a few advantages. First of all, it is more personal than simply "Greetings" or "Hi all". Secondly, if one of those people is the main recipient and the other is CC, or if one of them has a higher rank (say, he is the boss of the other), I can reflect that in my address by mentioning him first. Lastly, this formula can be easily adapted to many situations. If some (or all) of the recipients are female I simply write:

Dear John,
Dear Jane,

If I need to make it more formal, I simply write:

Dear Mr. Smith,
Dear Ms. Black,

And I can easily extend it to three or even four people:

Dear Mr. Smith,
Dear Ms. Black,
Dear Mr. Blunt,

Now, when I am addressing more than four people, I often do use something like "Greetings", "Hi everybody", "Dear clients", "Dear colleagues". However, even then I sometimes set the most important recipient apart by writing:

Dear Prof. Black,
Dear colleagues,

or

Dear Mr. President,
Dear Members of the Committee,

If I am addressing a few people who are well known to me, I would generally use:

Dear John, Bill, Jack,

If I am addressing a lot of people, or people who are not familiar to me, I would go with:

Dear All,

I rarely begin emails with a salutation. If I do, it is usually just the name - I have never transferred the pointless 'Dear' to emails.

If I wanted to put one in a group email, I suppose I would start with a word like "friends", or "people", or "folks", depending on the context and formality.

It's kind of a carryover from my medievalist hobby, but I really like using

Greetings,

or even

Greetings!

for emails to a group of people. It's also really handy for addressing a single person when you're unsure of that person's gender and/or title.

If you are working together on a project, then I rather like

Dear team

This can be appropriate even if the recipients include people from both your company and the client. It's a subtle reminder that you are all working towards a common goal.

More generally, I'd just use

Dear all,

or just

All,