Originally Posted by Dingus
In UK (I don't know about US) there has been a long standing convention that:
a) if you start a letter without using the addressee's name (eg Dear Madam) you finish it with Yours faithfully.
b) if you start with their name (eg Dear Professor Smith) you end with Yours sincerely. I don't think there is much difference between Yours truly and Yours sincerely. Yours truly may be less formal.
Personally I don't like Yours truly and I would never use it. I suspect that some people feel the same, so it may be safer to be sincere rather than true!
I would never use Sincerely on its own.
In business letters to people I know very well I might use Yours, Best wishes, Regards. If I did that I would always then only use my first name to sign, not my full name eg Regards, Michael).
Wandering off-topic for a moment there is an idiomatic use of Yours truly = I/me, eg "People always expect yours truly to do the nasty jobs!"