Diamond Geezer has a great post on how to start and end an email, with 44 comments at present. It starts Hi Reader and ends Many thanks dg.
I think this shows that there is no easy answer to how to address people in both formal and informal emails.
I hope this post doesn’t come across as prescriptive, because I have great doubts about all forms of address and closing.
In German, the problem is just as great.

First, in letters (British English only):
Dear Sir or Madam … Yours faithfully
Dear Mr. Smith /Dear John … Yours sincerely
In the law firm I worked in, we had this closing for clients:
Kind regards

In formal emails, you might start
Dear…
And close:
Best regards
Kind regards
Is this right? I rarely write formal emails in English and I have been known to close
Yours sincerely

which may be a no-no in email.

Now the emails to friends, acquaintances and forums.
I usually start:
Hi
Some write
Hello

To a forum, I often start without a greeting.

To close, I usually write
Regards
Some write
Kind regards
Best regards
which seem awfully formal to me.
Then there are
Cheers
and if one wants an answer
Thanks
Many thanks
TIA
MTIA
Best wishes
I particularly liked dg’s comments on Take care.

Take care. Whereas this one’s not so good. It may be only eight letters long, but there’s an unspoken hint within that something terrible is about to take place. You might as well end your email with “Watch out!” instead. It’s much too negative for me, and I’d hope for you too.

But I suspect that Take care is more common among Americans.

Now about German. First, formal.
A potential new client might write:
Sehr geehrte Frau Marks … mit freundlichen Grüßen /freundlichen Gruß
or
Hallo Frau Marks
Guten Tag Frau Marks
This is less formal and might come from the secretary of a client one already knows.
After some time, the client might want to be more friendly:
Liebe Frau Marks
Hallo Frau Marks /Guten Tag Frau Marks
Beste Grüße
Herzliche Grüße
Viele Grüße
Not everyone likes Viele Grüße, but I quite like it, and in any case I follow the client’s lead.
Non-Germans should note that the ß character has not been abolished – Gruß/Grüße and Straße are the most common pitfalls (except in Switzerland, of course).

Now in German to friends, acquaintances and forums.
I do have a difficulty here, because I have found German forums more formal than American and British ones. Maybe that’s because I was on CompuServe much earlier than on German forums and they seemed slower to relax. I have had my knuckles rapped and been thought to be intentionally rude for writing to a forum without a greeting. This was obviously an offence against German netiquette. I don’t know if that is the case any more, but I have an uncomfortable feeling when I write to a German forum.
So some write
Liebes Forum
Liebe Mitglieder
or some variation on the forum’s name.
Otherwise it’s down to
Hallo
Moin
I don’t feel northern enough to use Moin (which is not limited to the morning)
I usually close with
Gruß
but always feeling it is a bit abrupt.
I have not got used to the increasingly common
Liebe Grüße
which feels overfriendly to me but is possibly becoming standard.
I have just checked my inbox and found one
Schöne Grüße
and one
Mit kollegialen Grüßen
(this reminds me a bit of Mit sozialistischem Gruß in Goodbye Lenin).
It’s also, I remember, fairly common to mention the weather in one’s location:
Mit verregneten Grüßen aus Köln
Mit sonnigen Grüßen aus München
or if one wants a reply to a question
Neugierige Grüße
Is this done in English? I certainly avoid it.

LATER NOTE:
It’s been pointed out by a commenter that MfG is a bit of a no-no, especially in formal correspondence.
That reminds me of some abbreviations widespread in informal contexts. Thnx rather irritated me because it’s scarcely shorter than Thanks.

Lawyers among themselves use Mit kollegialen Grüßen (see comment). I sometimes have to translate this into English, and the equivalent is just Yours sincerely or Best/Kind Regards. There’s a lovely heated discussion on this on the LEO forum.

And I forgot to mention the direct address I often use on forums: just the name of the person addressed, without any ‘Dear’.