Not the contents nor to/from whom, just the date.
August 2002 for me.
12/13/2002
I switched from Netscape to Outlook in 2001, so I have stuff from 2001 in my active Outlook folders.
I still have my email folders from my Netscape account archived; emails in that probably date back to 1996 or so, but access is a bit tedious.
The oldest one I could find so far is Feb 13, 2006.
If you include archived emails, it’s going to be ca. 1995.
Emails actively available directly from my email client are likely to be more like 2003 or so.
Gmail, 2007-ish.
Work email, 4/18/2011.
That’s close to my story, too. The original internet-ready computer was a Compaq circa 1996 and when it gave up the ghost I had to start afresh with email on the new Dell. I could possibly retrieve older emails from floppies, if I just had to.
At work we used cc:Mail and Lotus Notes, but I never had the capability of retrieving those once I left work in 2000. Even so, the oldest emails I could hope to recover would have been from mid-90’s. (I’m not even counting “email” I would have swapped on the Commodore 64!)
I have to double check if I have any earlier, but I have every non-spam personal email received since August 1996.
Jan. 5, 2008. That’s right after I bought this computer.
Can anybody beat these on your current computer?
November 2005. I could probably dig up older ones if I try
December 20, 2011.
I had to change email addresses after nearly a decade at my old one because I was getting tons of spam and email chain letters.
25/4/2004. Welcome from the Gmail team.
10/21/09.
Everything earlier than that is archived on some other hard drive somewhere. Or not at all. I don’t usually bother with keeping old emails around.
That’s not really on your computer though. I don’t think that webmail counts as far as the OP is concerned.
That’s true. I was looking for things on your own current computer.
But how else will I be able to prove that my cataloging professor told me the paper was due on 10/3/95 and not 10/1/95 like she’s now claiming? 
Over the years I have transferred most of my emails to the Outlook Express file on my current computer. The oldest one is one I received when I had a Compuserve account, dated March 23, 1993.
The new one to beat! (Unless I missed an older one.)
No. I have one that’s 12/31/1969, and it’s not even archived.
I believe we have a winner.
Damn. What system was that? CTSS?