If you address a letter simply as "Dear,", you are actually using a vocative to a person you are calling dear. This would be the same as starting a letter, "My dearest love," such as the famous Sullivan Ballou letter.
I can think of no case in which a formal letter, sent to an institution, would would ever make logical sense.
That said, if you started a personal letter with "Dear," you are calling out to your dearly beloved.
Also note, if you are writing a formal letter, the salutation should be followed by a colon, not a comma. Thus,
(Or for that matter To the John Deere Company: or To Whom it may concern: )
Of course, if you follow the link, you'll see that Sullivan Ballou himself actually punctuated his very personal letter with a colon. This is no longer appropriate in Standard English.