The first "spam" was sent on ARPANET, mid 1978, metacrawl for "Gary Thuerk". I didn't get my copy of the email, alas, or I would copy & paste it here. Gary got yelled at, none of the rest of us ever tried anything as daft.
I remember a student at Stanford sending every email account on campus a "wanna buy my bike?" email back when I was stanford!sail!vax!jake (name changed to protect the guilty; I'm archived at DejaGoo under the real name) ... Probably 1982 or thereabouts. He got yelled at, loudly, and had computer privileges revoked for the rest of the year.
After that? Probably the first real spam was on Usenet in late 1993 or early 1994. (Religious crap, and a bot kibozing on the word "Turkey"). Followed, of course, by the infamous "Green Card Lottery" spam.
For modern email? Soon after Usenet ... I'm guessing late 1994 or early 1995.