I’ve had my personal never-give-it-away and more public email addresses since 1997, when I bought my domain name. The more public address – still never posted online – gets spam, but most of it is filtered by the eight or so RBLs (realtime blacklists) all mail passing through my server is checked against. The personal email almost never, ever gets spam.
Hotmail, since the late 90s. It was my third address–I’d had one hotmail account previously which I locked myself out of, then I switched to Goplay until it went bankrupt. After that I created my current address which I still use almost exclusively (I have another one through school but I rarely check it, let alone use it. As of yesterday there were 850 unread messages in there).
I got my AOL account in 94. I still use it.
In 1997, I got a Yahoo! address that is my first name and last name @yahoo.com, no punctuation, no numbers. I like it because it’s easy for people to remember. I still use it as my only personal email address. I get a lot of spam, of course, but I find that the spam filter on Yahoo! works pretty well for me.
I got my Hotmail address in 1995 and still use it daily.
I got my Yahoo! Mail address in 1996 and use it daily.
Since this is basically a poll, I’ll move it to In My Humble Opinion for you.
Cajun Man
for the SDMB
i used to have ao-hell which dated from 1995, but that’s long gone. the current oldest is 2000 with yahoo, but i have four additional yahoo addresses for different things, an inactive hotmail, two outlooks and maybe a catv broadband, which i never use.
My oldest address is my Yahoo address, which I got in 1996 – although technically it was a Rocketmail address at the time. 
When Yahoo & Rocketmail became one I had the option of keeping the @rocketmail part, but I went with @yahoo because it’s shorter. That address has stayed with me through 11 years* of different jobs and ISPs, and is still my primary one.
If the OP doesn’t mind a related hijack, I’m curious about how many e-mail addresses everyone has. Right now I have 4: Yahoo, school, work, and Comcast.
*It’s freaking me out a little to realize that I’ve had e-mail for 11 years!
My oldest address is the one I use for my website. I’ve had it since late 2000. It gets quite a bit of spam, because for a long time it was posted on every single page of my online journal. This was back before I had a clue about spam avoidance. I still keep the address around, because it’s useful for my website, and also because my ISP is pretty good about implementing good spam filters these days. The inbox is still usually about 75% spam on an average day, though.
My primary email address is the one I’ve had since 2004, and I am paranoid to a fault about keeping spam out of it. I deliberately chose a user name that was a combination of numbers and letters, and I don’t use it for online forms or purchases or pretty much anything at all over the Web. It’s for personal correspondence only. So far, so good; I’m going on 3 years of being spam-free. (Except for the occasional spam that comes in over a spamgourmet forwarded address, but then I just go to spamgourmet and delete the offending address and the problem is solved.)
I had e-mail on GEnie from 1989 until 1996. GEnie was like the original CompuServe, Prodigy, and AOL – mostly internal – but eventually allowed e-mail from any Internet source. GE sold the service to a bunch of sleazes and I had to get out.
My oldest current e-mail – and still my main personal e-mail – dates from around 1994 or so.
I’ve had a Yahoo account since 1999.
I’ve had my Hotmail address since 1996 or 1997 (pretty sure it was before I finished high school, anyway), and I still use it regularly. Surprisingly, it doesn’t get all that much spam - maybe 4 or 5 a day, and the spam filter catches most of it. I’m slowly making the move to Gmail because I like that it automatically saves sent mail, which comes in handy. I’ll keep the hotmail one for use with MSN Messenger, though.
I change about once a year, just to get a spam break for a while.
I always worry about the changeover until every one of my regular contacts has used the new address.
My first Internet email would have been '95 or '96. Prior to that, we had internal mainframe email systems since '85.
My Yahoo account is from 95 or so, right after Yahoo went live. It’s still doing fine, not too much spam gets through the filters.
My first publicly accessible email was from Digital back in 1985, on a backbone machine no less.
I got my Hotmail account in 1996 and still use it today.
I started in 1985 or so as asknott@; I have switched companies a few times, but I’ve been asknott at every service provider. Right now, it’s asknott@insightbb.com.