Ever since man learned how to communicate, he started looking for ways to improve communications. And ever since women learned how to communicate, we've had spam, and men looked for ways to filter communications. This is just human nature. (Look, it's a joke. But there is a certain truth to some people/genders communicate more than others, and others want to learn how to filter wheat from chaff).
We could probably trace email back to smoke signals or the jungle drum; that was how man first started trying to communicate over long distances. Later there was semaphores and flags and pennants for ships (or even castles); since open fires were not only unsafe of wooden vessels, but also the winds made smoke signals hard to manage, and sound doesn't carry very far. Of course some nit pickers will whine that wasn't "electronic" so doesn't have the 'e' in email.
Well then, we can trace email back to the turn of the century and Morse Code and the telegraph, or the later telex or ticker tape systems. Of course other detail freaks will complain that with Morse Code and the telegraph you had to be listening to the message as it went by or it was gone; it was a broadcast media and not medium that you could get and read or trash at your leisure. Of course that's not completely true; we just used to have humans transcribe that message for us and then storing the pieces of paper. However, there is a point in there and the paper and human aspect wasn't completely private or electronic. And the telex systems did meet those criteria but couldn't be initiated by just any user; often requiring specially trained operators and expensive and dedicated hardware. So for purposes of discussion, let's think of email as computer based store-and-forward type file solutions, that couldn't possibly have predated computers themselves.
During the 60's computers started becoming more popular, at least in a few businesses. They were also expensive; so one of the first things you wanted to do is "time share" or have many users using the same machine for many different things. Of course, if many people were using a machine, then the next thing you wanted to do is give them their own areas of the machine (file directories or folders), so they wouldn't touch each others files.
Now a memo and an "in-box" isn't a big leap from there. Each user has electronic folders, why not have a folder for each person that other people can drop memos or notes into? Viola; this was instant primitive email without any new software written. If it was a public folder that others could read, it became an electronic bulletin board or newsgroup. Once users started doing this, it wasn't long until specialized programs were written that could manage things better.
Of course that wasn't the only simultaneous evolution path. At the same time users were doing that, computers were also evolving so they allowed many users on at the same time from different terminals. Earlier systems were "batch" jobs, where everyone submitted their stuff in a queue (line) and things got executed one after another. But since the newer systems had many users actually using the same computer at the same time, why not allow one terminal (user) to send messages to another terminal (user) like the phone system? In some ways, this software was easier to write than full email systems and the "live chat" or point-to-point communication was also a very early and instant success.
All the solutions evolved separately and simultaneously, while borrowing features from each other. So you had the file based bulletin boards and private messages as well as the live messaging solutions, all growing at the same time. But all those Programs generally only worked within a single computer; it wasn't really a network, it was usually just all users for a single time-shared computer.
Of course as some companies and organization actually could afford more than one computer in a location, or had two computers in two separate locations, they wanted to figure out ways to connect them and make them talk to each other. Each computer manufacturer did this with their own proprietary networking hardware and software; and it wasn't soon after that when they made all their communication and messaging software talk from one computer to another as well. So users could log into any terminal or machine, and get their files from the other one, or see their messages. Often early email was called "network mail" because it was a way to send mail on that one network.
During the 70's and 80's, two simultaneous things started happening; microcomputer evolution and network evolution.
The Apple][, Commodore Pet's, Tandy, Kit computers, and soon after Atari, Texas Instrument and Timex computers in the late 70's brought computers into homes. They weren't cheap, but they were affordable. And modem's had existed for big computers, and were soon adapted to their less expensive cousins; mostly so that you call into works big computer, and turn your $2000-$3000 computer, into a $500 dumb-terminal and do some work from home at very slow speeds. These were the days with 110 or the "faster" 300 baud modems, when users could easily out-type their network, and had to wait constantly for the network to catch up.
Well, the hardware to allow these home computers was in place, you could call into work, and be a terminal, and even get your work email and work bulletin board items; but what fun is that? And since most corporate networks were tied to proprietary hardware or systems, you often couldn't get messages across systems in the same company, let alone the pipe-dream of one companies hardware talking to another. So private services started popping up.
Often, people would just dedicate a computer to allow many people to call in and read all the public messages (bulletins), and discuss various issues, and send some memos only to certain individuals (private emails). When they became sophisticated enough (early 80's) to allow multiple people to connect at once, the live chat features were added as well.
It wasn't long before these simple little private bulletin boards or computerized party-lines, weren't snapped up, or duplicated by companies that wanted to make a business of it. MCI Mail, EasyLink, Telecom Gold, One-to-One, CompuServe, AppleLink were all created. Later AOL (America On-Line), Genie and others as well. These allowed not only individuals to talk to one another for fun, but also allowed businesses to send messages to each other; and since they weren't quite run out of some guys garage, there was more security that someone wasn't reading your private messages for fun, as was so common on the private bulletin boards.
Ubiquitous Public Networks
Now all these networks existed, some private, many public. And there were many users; millions of personal computers had been sold. But the networks weren't standardized; a few could send to each other, but that just wasn't the same as a standard.
The ARPA/DARPA had funded network research and is what we called the early "inter-net" (Inter-connected networks); but this was expensive and complex, and mainly used by Universities and Government only all during the early evolution of microcomputers or personal computers. It wasn't until the mid to late 80s that things started changing.
Many private companies like IBM, HP, Xerox and Digital Equipment all started making their networks also work with the college and government stuff. Their private stuff was often better in features and functions; but as people could only use a subset of those functions to send through to other computer networks, we actually sort of went backwards so we could go forward. All new companies that were coming on, couldn't afford to reinvent the wheel and develop their own network stuff, so they started borrowing from the hardware (Ethernet) and software (Internet or TCP/IP), and things started standardizing.
The more they started standardizing, the faster the ball got rolling and the more momentum it gained. People wanted to be able to send messages to anyone, on any network; and not just have hundreds of private networks; and the private bulletin board based systems were quickly replaced by public websites and email.
A common misconception is that the Internet created email, mail lists (bulletin boards), file sharing or many other things. It didn't. Email existed before the Internet, and was popular before the Internet was. There is common story about Ray Tomlinson and Bolt Beranek and Newman (BBN), and how they created email in 1971 with SNDMSG or READMAIL. But that wasn't creating email, that was just the first email on ARPANET, which later became the Internet; and requires us to ignore all the innovations that came before or since. The same goes for bulletin boards, live chat and most other things. Heck, network gaming existed in 60s before the Internet. So don't buy blindly into the Academia or government propaganda about how we have them to thank for what was happening anyways; their contributions helped, but aren't the whole story. It was the popularity of computers and private networks that drove the success of the Internet and it's email protocols, and not the other way around; the Internet just provided a "good enough" framework for all these private solutions to standardize on.
The future of email is probably going to be centered around its ability to find you and deliver itself (smart instant messaging). Right now, most email is polled; you need to check it. If you don't check your email, you'll never know when you have email - and you have to check it on the right system. I think in the future, there will be ways that you register your devices and email messages that are sent will get to you; connect to your computer, phone or PDA and tell it that you have email, instead of waiting for you to ask it. And it will find the right device, and once read on one device know to not badger you on the others. Just basically increasing the convenience and instantaneousness of delivery; while blurring the lines between live chat, email and lists even further.
I also think devices will blur; land phones, wireless phones, computers and PDA's all support communications; but where does one end and the other begin? If you think that is hard to define now, just wait a few years. The same for types of communication; audio and text (and files) are currently popular. Video, collaboration, presentation and software interconnection is less popular because it is needed less often; but increasing, and is likely to keep increasing. What if a $2 chip allowed you to do everything and connect up wirelessly no matter where you are? Moore's law implies that isn't far away. How many devices would you expect to see that offered communication capabilities? And what will these messages be used for? Appliances that tell you when they need repair, cars that tell us when they are stolen and where they are; these aren't science fiction, they are already happening.
Humans have always communicated. There has always been personal communication, public speeches; live demonstrations and posted posters and placards; going back to cave painting. Electronic versions of these are just part of the natural evolution of communications. Humans communicate, so devices that help us to do that effectively are quite popular. That puts a motive on continually evolving and improving that communication. I don't think we've yet reached the end of that evolution, and tomorrows devices and forms of communication will make today's look primitive.