I started in 1990, and not only did I not have an email address, I didn’t have a computer or use one in a computer lab for my entire college career. Instead, I had a Smith-Corona word processor with a disk drive and a six-line screen. I could load papers from the disk and print them —took two minutes a page.
College Freshman in 1992; first incoming class to have email addresses assigned as part of orientation. It was my first email address. Still works, sort of.
It still used hidden commands that you had to memorize, though. I much preferred either having a menu on screen or a list of commands when you were in command mode.
Wouldn’t surprise me at all, which is why I specified community college. We CC alum tend to get forgotten in discussions about “college students”. 
Regional state university in 1994, we had email. If you didn’t have your own computer, and they were rare, there was a lab of dumb terminals in each dorm and scattered around elsewhere.
ETA lots of fights over those terminals between “legitimate” users and MUD/MUSHers. Any other VikingMUD players?
My major public university (UCF) had e-mail for every student who wanted it by 1994 at the latest, and required every student to sign up for it (in order to enroll for classes) by 1997.
My final semester at the University of Wisconsin-Madison was the spring of 1989; at that point, e-mail wasn’t yet widespread there, and I certainly didn’t have an e-mail address. (Then again, I was in the School of Business; it wouldn’t at all surprise me if students and faculty in the tech-related schools had had e-mail for years at that point.)
I’d been using an acoustic modem as part of my work-study job, to pull down information from University databases, as early as 1984 or so, but that was just dialing directly into a school computer and sending a series of commands, then waiting for the data to slowly print out on a dot-matrix printer.
When I started my first job in '89, I got my first e-mail “address”, but that was an internal system (we used a computer system called Metaphor, which was very much based on the original GUI from PARC); we could send e-mails to each other within the company, but not outside of the company.
Wait, did you just call vi intuitive? You are talking about the same vi I know of, right? The one where, even if you can figure out how to start typing, you’d never guess how to go from there to doing anything else (like saving or printing), and couldn’t find out, because getting help was another thing you couldn’t do from there? Let me tell you, if I’m ever in a terminal-only environment, I’m going to use something sane like pico, because even though I could learn vi, it’s just so much easier to just use something that really is intuitive.
As for community colleges, I taught at one last year, and it goes both ways: There’s 100% an expectation that you’ll use the college-assigned e-mail, but lots of luck getting them to actually set one up for you.
Maybe there were a few small colleges excepted, but I would be astonished if there was any institution calling itself a university that did not have email for any student who requested by 1990 and probably a couple years earlier. Here is what I know for certain:
When my son started out as a freshman at Princeton in 1984, he had been playing with computers for 2 1/2 years (mine), had written a couple of quite playable games and was generally quite experienced. So instead of bussing tables he worked late nights on the help desk in the computer center. At that time, Princeton was on bitnet and anyone who asked could get an account. McGill, where I was, actually was on bitnet but only computer center people could use it. My son became aware of this and, every night, he would send an email to the head of telecommunications at McGill asking why they didn’t open up bitnet to everybody. They didn’t answer him, but along around US Thanksgiving, that is late November, our computer center opened up bitnet to all of us and I got an account. After that, our son wrote us regularly. Equally important to me was that suddenly I had an easy way of communicating with my coauthor at Case Western.
Meantime, my daughter at Williams College got a bitnet account about a year after this, maybe late 1985 or early 1986. Every student could get an account, although probably few had much reason to. By the time, my younger son went off to college in 1991, bitnet was gone and email accounts were issued as a matter of course, for internal communication if nothing else.
I graduated from well-endowed Big 10 university in 1991 and a student having their own PC (or Mac) at that time was somewhat of a novelty. I’d say maybe half of my friends had a computer, and most of them were in the school of technology. Your average liberal arts student probably didn’t have one. There were computer labs on campus that were regularly used for papers, etc.
Even for those who had computers, internet connections were even more rare. My sophomore year roommate upgraded from a 1200 baud to 3600(?) baud modem and guys from around the dorm would come by to see how fast it could connect to the library’s online card catalogue. Things were a bit more advanced two years later but still, having email in '91 was the exception and not the rule.
Everybody had an email when I was in Undergrad around 92, it was required. And yes there were some very good deals to get your own computer, but if you didn’t you had to spend a good deal of time in the labs. You had an account that allowed only so much time logged on to external systems, and in my first couple years was fairly small and you had to be strategic.
This was at University of Michigan, which was highly involved in the early days of the internet, from MERIT to NSFNET etc.
Indiana University, mid-90’s. We were all assigned a .edu email address that we (most easily) had to access via the dumb terminals in the common areas of our quads (dorms). In my case, that would have been about 4 terminals per thousand students. Unfortunately, some professors seemed to have been time-travelers and would email us the morning of class to let us know that class/lab was cancelled/relocated/whatever as if we had smartphone alerts. I was a bit more tech savvy than most, but I could never get my email to work on my smokin’ 486 DX personal computer in my dorm room, even with outside help, and certainly could not check my email every morning before my 7:20 Scheme/LISP class (do they even teach that anymore?!).
I started college in 1976, and was immediately given an email address. This was in the engineering college at the University of Illinois. I don’t know how universal it was, but we all had them. The format was different that it is now (no xxx@zzz.com), but it was email and we all had to have it.
I graduated college in 1995 but didn’t get email or know anyone who had it until I started grad school in 1996–then it was like suddenly everyone had it. As for computers in college, I just spent a crap ton of time in the computer lab.
In many Aus universities, you got an email account if you had a computer account. But (1) Until email became necessary, many students did not have computer accounts, and (2) Until email became necessary, not all students were told how to access their email account.
Aus is notable because non-university email accounts lagged several years behind the USA. For the first couple of years, there was no public access to the internet at all. You worked for an international company that paid for an internal connection to a company intranet, you were a high-level geek using an international phone call to connect to an American provider, or you were a university member. The universities were connected to a single internet hub at the University of Melbourne, that did not permit private or commercial traffic.
Eventually one man at Melbourne University somehow got control of the international connection, and became the king-pin of Australian internet. I never knew how that happened, but I do remember the odd restrictions he imposed, and that you effectively needed his personal approval.
You are thinking of Robert Elz. It is a bit more complex than that, but Robert was a key player in the early days. Along with Piers Lauder and Bob Kummerfeld (and a host of other players.) Robert was famous for getting control of the .au TLD, and it was on his personal say so that anyone got a domain name inside .au - which included .com.au - which raised a few eyebrows and dispute. Eventually his control was moved over to Melbourne IT, which on the back of that control became quite an earner for Melbourne Uni.
The early days of email in Oz, were as I wrote above, significantly boosted by ASCNet, later to become MHSNet. This was down to Piers Lauder and Bob Kummerfeld. In addition to ACSNet, CSIRO had an intranet, and provided some of the backhaul, and of course many private companies had early intranets. DEC of course had DECNet. There were gateways (or various legality) between some of these. ASCNet was useful as it worked in the face of intermittent connections - so you could have a periodic dialup link established to transfer mail a few times a day. It also supported file transfers, and had a lot of neat features.
Bah - accidentally hit post - continuing from above…
Slowly the Oz universities established a fully functioning internet, using Internet protocols, and in 1986 the first permanent connection was established across the pacific connecting Oz to the Internet. For a while the universities were way ahead of the game, and commercial provision of Internet connections was essentially zero - so the universities provided connections - in a manner that was somewhat ahead of the regulations controlling telecommunications (translation - it wasn’t really legal). It was in this time that the TDL control went to Robert. Once the commercial providers had caught up with this whole Internet thingy, it al became much more regularised.
Wrt to OP, this strikes at the heart of the question about having “email”. An email account that allowed communication with other students and staff at an institution is a different beast to one that allowed communication with people at other institutions, perhaps on the other side of the planet. US universities were at the head of this, especially with UUCP email hacked together between institutions, although the UK was doing its own thing in parallel (X.400, colourbook etc) but it wasn’t until everyone settled down to an IP based worldwide network and SMTP that universal email became a true reality.
Having an email address was not correlated with having a computer. You did your email at a terminal that might have been in the dorm or the computer center.
Australia was a special case. In 1987 and Australian mathematician at a major conference in my area compiled a list of postal and email addresses of all the attendees. He said he would get the list typed in a computer file and we asked him if he would send each of us a copy (we all had email by then). He was shocked at the request. He explained that it was all controlled by the Australian PTT who charged $1 a page for handling email at least overseas. I don’t know what a page was but our colleague was unwilling to spend a couple hundred dollars to send it out. We were astonished at the cost and he was astonished that we were not charged at all. Eventually, he sent out one or two copies to someone who circulated it generally.
I guess the PTT was protecting their turf but they were also seriously preventing Australian researchers from participating internationally. I don’t know when they lost control.
University during '90-'93. We had email but the only thing it was used for was getting library overdue alerts, and tuition due alerts. No students had computers that could dial in to check email, so it was a manual effort of walking to the campus computer lab, logging in, and checking it.
My last year, the department and some students had a play-by-email game of “Space” going that was incredible fun, a build ships, expand, and conquer the galaxy thing. You submitted daily ship build and move orders by email, and got results the next day. Weekly fan-fold printouts of the map of the galaxy and game state were printed out at the computer lab.
University of Washington, entering freshman in 1992.
Was given an email address when I showed up along with instructions on how to dial into their network. Most rooms on my floor in the dorm did have a computer (I brought one to the room, my roommate did not have a computer). There were many computer labs spread around campus (and a big one that was open 24 hours) if you didn’t have your own.
Don’t recall the email address ever being used for official communication from the school or expected communication between students and instructors (though it was an option if everybody was on board).