Email has been around for a long, long time. Besides the major players, there were any number of mail and public post networks that ran on hobbyist bulletin board systems (FIDONet and WWIVNet are two that come to mind on the BBS end, and BITNET was a popular academic network before TCP/IP took over the world).
Toward the end, there were gateways between (almost) all of these systems that worked more or less reliably. You had to keep a text file handy to figure out how to mung an address on network #1 so that it would delivered to network #2.
For instance, a WWIVNet user could send email to foo@bar.com by sending it to foo#bar.com@5XX, where 5xx was a WWIVNet node number in the 500 range (these were reserved for gatewaying purposes). An Internet user could send email to 23@9073 on WWIVNet by sending it to 23-9073@(some site that was running the gateway software).
Similar address rewriting hacks were used for the other networks. Some were pretty straightforward -- I remember CompuServe used addresses roughly like 888,923423. To send mail from the Internet to CompuServe, you just had to change the comma to a period and tack @compuserve.com on the end. Others were pretty arcane.
Probably more than you wanted to know. :-)