Well, email used to be like that, as Clifford Stoll will tell you. And there's no reason why it couldn't be like that again, if you want to do some sort of Colonial Williamsburg E-Maile reenactment (that's the hipster Williamsburg, not the one in Virginia). Old standby mailtothefuture.com has been shut down, but mailtothefuture.org has sprung up in its place. All that's missing is the random element; you have to specify your delivery time to the hour, which is way too precise for these purposes.
HassleMe has a nice randomness element to it, but that's because it's emailing you periodically, reminding you to read an improving book or whatever. Wed Jan 09 2008 23:20:
Evan and I were brunching at our accustomed table and bemoaning the death of the personal letter as an art form. Oh, it's so much more intimate than email. Except I never got around to sending any of those letters, and once my mom got email we talked a lot more. So bah to the personal letter. But Evan had the retro Stockholm syndrome we old-timers sometimes get when we think about old technology. He liked the way you didn't know when your letter would arrive, when there was a several-day lag time and a day or two of uncertainty on either side.