It's a very old fashioned term. In a formal emails people usually write "Yours sincerely" or "Kind regards"

This is an interesting question. I would respond that "cordially" is a formal word in ending a letter, but the medium called e-mail is quite informal. I never use it in English.

Never. Cordially is used when writing a very formal business letter. It is very formal and old fashioned.

No I don't.

I would only expect to see (or use) it in a very formal invitation: "You are cordially invited to..." If you use it to finish a work email or letter ("Cordially yours,") it gives a mixed message of high formality as well as upper-class warmth. I ask my business students to always think about who they are sending the message to before signing off their emails, as their sign-off does indicate to the reader how you think of them. One generic ending for every message is not appropriate. This is the person I think of when I see "Cordially yours": http://www.youtube.com/watch?v=pDl4ye22U-E