The expression "yours faithfully" isn't old fashioned. It applies to any letter where the recipient is unknown. Hence, if you begin with Dear Sir/Madam you end with Yours Faithfully. If you know the person in a formal context, or at least their name/sex, then you write Yours Sincerely or Sincerely. Ergo, if it is a letter to a lecturer, it would begin Dear Dr. Euripides and end Yours Sincerely. In cases where you are on a first name basis with the recipient, you can then use a more friendly context specific greeting: kind regards, best wishes, all the best, etc.

Fact. 

Faithfully? Many people do not believe in faith. Regards is personal. Wishes, many people believe that wishes do not exist in a deterministic universe. Best, is the only way to end it.

The grammar teacher did indeed have a point.  The correct usage is either "Best wishes" or "Kind regards" - but never a combination of the two "Best regards" - which is at best clunky and at worst reveals a lack of good grammar.

It is also fine to use "Yours sincerely" although this would normally be applied to a letter rather than a (less formal) email.

Save your fingers. The sender's regard or respect (hopefully high) for the recipient should be evident from the content of an email. Paper communications are maybe a little different being inherently quaint and not very respectful to trees!

David Kirk

I have never seen anyone end a letter or e-mail with "My Best" and have heard Academics end with "Best".

You are right MrP, it's very disconcerting when someone ends with Best and in my case its even more because she has ended it with "My Best". I'm dying to figure out what she actually meant. So, it would be great If you guys can solve the mystery of what "My Best" means. Thanks