The traditional British style would be to use yours faithfully for letters starting Dear Sir , Dear Madam , or something grander such as My Lord , and to use yours sincerely for the slightly less formal letters starting with a name such as Dear Mr Smith , Dear Baroness Jones ,
Dear Sir James etc.
The point of both is say that the writer has been telling the truth.
There are some minor religious connotations in yours faithfully so for example Rothschild's investment bank will often sign yours very truly .
There was an old-fashioned ending along the lines of
I have the honour, Sir, to remain your obedient servant sometimes shortened to
I have the honour etc.
but that is now rarely seen.
Best regards is clearly informal, and should be used for informal contexts.
Examples might include email or letters starting Dear Jane
english.stackexchange.com/users/4333/Henry
When working in England, I've found that "Regards" is most common, even amongst parties that have a good relationship.
When working in Australia, "Best regards" is much more commonly used.
Using simply "Regards" would seem quite standoffish.
I'm not sure which is most applicable in Denmark.
english.stackexchange.com/users/1963/Alex Angas
I was always taught to use 'Yours faithfully' in letters when addressing someone I didn't know, and 'yours sincerely' for people I did.
However no such rules exist for emails, and using either of these valedictions would seem quite stuffy and overly formal.
I'd use them only (if you wished to use them at all) in formal, written correspondence.
'Best regards' is a fairly standard valediction that is neither too formal or too informal and would be suitable for any business email.
Tragicomic's comment on your question gives you a number of suitable alternatives.
english.stackexchange.com/users/3876/gpr
The formal rule, at least in Britain, is that if you're writing a letter to a person whose name you don't know, you start with "Dear Sir or Madam", and you end with "Yours faithfully".
If you do know the name, you start with "Dear Mr X", and end with "Yours sincerely".
However, as you note, "Best [or kind] regards" is much more common these days.
But again it would only be used when you know the person's name - and I would probably say, only when you actually know the person themselves.
english.stackexchange.com/users/308/Daniel Roseman
I'm surprised no one's mentioned Yours truly .
It strikes me as a shade less officious than yours faithfully but not as boilerplate as Best regards or its weird sister, Best .
english.stackexchange.com/users/17772/fortunate1
Yours faithfully , used to end a letter, is chiefly British and it used in a formal letter to someone whose name you do not know.
Best regards can be generally used, and it would be my preference.
english.stackexchange.com/users/252/kiamlaluno
There is a trend that I approve to stop using those complimentary openings and closes.
They are relics and literally are usually ridiculous:
Dear Sir:
Your employment will be terminated on 31 March 2011.
Yours faithfully.
english.stackexchange.com/users/6785/caxtontype
What I see increasingly in e-mail correspondence is 'BR'.
It seems to me that this, along with the strange and pointless-seeming 'best regards' itself, is essentially business-speak and meant to make the correspondence, and by extension the writer, seem 'professional'.
I can't bring myself to use it myself, so in such correspondence I tend to sign myself best Christopher
But I doubt it will catch on.
english.stackexchange.com/users/42103/Christopher Lord
Despite the name, emails are not letters.
Many people try to equate the two, but they are completely different mediums, and different rules have historically applied.
In former times many people had very limited bandwidth and email storage capacity, and would in fact get annoyed (if not downright hostile) with people who put large amounts of unnessecary information in an email.
This includes salutations (which are redundant with the email's automatically attached header), and excessive or unnessecary signature/footer information.
Return contact information used to be common in footers, just in case it got somehow mangled in the email header.
However, it has always been considered common etiquette (aka: "netiquette") to keep footers to 4 lines or less.
A lot of this has been formalized in RFC 1855 (section 2.1.1 is for email).
These days those issues are by-and-large moot.
However, getting right to the point, and quitting when you are done, are still considered better form that adding a whole lot of polite chuff around the meat of your conversation.
For further detail, you may consider picking up a copy of The Elements of E-Mail Style , although it is about 20 years old, so it may be a bit dated.
english.stackexchange.com/users/9186/T.E.D.
I've been taught to end business letters with "Yours faithfully" but I can see from my daily correspondence that "Best regards" is more commonly used but seems more informal.  What term should be used and under what circumstances when writing email these days?   NOTE:  If other terms exist too (for colloquial use or extreme formalism) I'd like to know that too.
When ending an email, should I use "Yours faithfully" or "Best regards"?
english.stackexchange.com
<formality><email><valediction>
english.stackexchange.com/questions/11661
english.stackexchange.com/users/4295/Thorbjørn Ravn Andersen
It is generally agreed that you should use "Yours faithfully" when addressing someone you don't know and "Yours sincerely" when you do know the person. "Best regards" is seen as informal and should be used for informal contexts, although some may feel that it is suitable for any business e-mail. "Regards" is also commonly used although it may seem quite standoffish to some. "Yours faithfully" is the traditional form of salutation to end a correspondence. "Dear Sir/Madam" is usually the opening one. It is suggested that these are for formal use and suggested the writer has been telling the truth.  There may be some minor religious connotations. For informal correspondence "Best regards" should be used even for letters beginning with the formal "Dear" . "Regards" is also another common form, but for some may seem a bit standoffish. Some believe "yours faithfully" is used for people that are not familiar to the writer, whereas "yours sincerely" is for those who are. "Yours truly" is another option and not as formal as "Best regards" or the truncated form "Best" sometimes used. There are some who believe all these forms of salutations are relics of the past as with emails, a lot of the content is already present in headers. Finally, some people believ style is more important than anything and the reference book is the "The Elements of e-mail style"
It is generally agreed that you should use "Yours faithfully" when addressing someone you don't know and "Yours sincerely" when you do know the person. "Best regards" is seen as informal and should be used for informal contexts, although some may feel that it is suitable for any business e-mail. "Regards" is also commonly used although it may seem quite standoffish to some. The formal rule in the UK would be to use 'Yours faithfully' where you do not know the recipient 'Dear Dir or Madam', but otherwise 'Yours sincerely' as a slightly less formal ending. 'Yours truly' is another fairly formal ending used in letters. Email is less formal, and other endings like 'Best regards', often shortened to 'Regards' or 'Best', are often preferred.
Traditional British style would be to use yours faithfully  for letters starting  Dear Sir/Madam , or something grander, eg My Lord. Use yours sincerely for less formal letters starting with a name such as  Dear Mr Smith. Best regards or regards is a fairly standard valediction that is neither too formal or too informal and would be suitable for any business email.      "Yours Faithfully" is chiefly British and is generally used when writing a letter to someone that you do not know. "Best Regards" is much more common and generally accepted, although  it may appear a little informal to some.
Despite the name, emails are not letters.
However, getting right to the point, and quitting when you are done, are still considered better form that adding a whole lot of polite chuff around the meat of your conversation. Best regards can be generally used, and it would be my preference. This includes salutations (which are redundant with the email's automatically attached header), and excessive or unnessecary signature/footer information. Examples might include email or letters starting Dear Jane There are some minor religious connotations in yours faithfully so for example Rothschild's investment bank will often sign yours very truly . Many people try to equate the two, but they are completely different mediums, and different rules have historically applied. Using simply "Regards" would seem quite standoffish. For further detail, you may consider picking up a copy of The Elements of E-Mail Style , although it is about 20 years old, so it may be a bit dated. Best regards is clearly informal, and should be used for informal contexts. Yours faithfully , used to end a letter, is chiefly British and it used in a formal letter to someone whose name you do not know. In former times many people had very limited bandwidth and email storage capacity, and would in fact get annoyed (if not downright hostile) with people who put large amounts of unnessecary information in an email. However, as you note, "Best [or kind] regards" is much more common these days. Despite the name, emails are not letters.
Yours faithfully is the traditional UK form Informal forms and "regards" Regards When to use the forms. Use of Dear Difference emails/letter Style above substance.
The formal rule in the UK would be to use 'Yours faithfully' where you do not know the recipient 'Dear Dir or Madam', but otherwise 'Yours sincerely' as a slightly less formal ending. 'Yours truly' is another fairly formal ending used in letters. Email is less formal, and other endings like 'Best regards', often shortened to 'Regards' or 'Best', are often preferred.
"Yours Faithfully" is chiefly British and is used when writing a letter to someone you do not know. "Best Regards" is seen as fairly standard these days and is not considered either too formal or informal. "Best Regards" could be considered informal by some.