After an extensive Internet archeology project involving retrieval of 20-year-old 9-track tapes from a warehouse in Pittsburgh, Mike Jones has traced the origin of the ubiquitous smiley :-) to a post on a Carnegie-Mellon computer system in 1982. Here's the idea that started the revolution:

19-Sep-82 11:44 Scott E Fahlman :-) From: Scott E Fahlman I propose that the following character sequence for joke markers: :-) Read it sideways. Actually, it is probably more economical to mark things that are NOT jokes, given current trends. For this, use :-(

It appears that the idea for a "joke mark" emerged after someone caused a panic by joking that one of the physics department elevators was contaminated with mercury. (There had been a previous discussion about what would happen to a blob of mercury on the floor of the elevator if the cable snapped.)

Interestingly, in reading the followup thread, many people began using doing it the other way (-:, which doesn't look very familiar to us now.