Fred Cohen's virus is believed to be the first piece of code ever referred to by the name "Virus". It was created as a demonstration of how self-spreading programs could be a threat while Cohen was a student of Leonard Adleman at the University of Southern California. Cohen later wrote his Ph.D. thesis on viruses.
The virus prepends itself to Unix executables. The virus is able to gain root privileges. It has no malicious routines and does not violate user's privacy. The virus is able to spread across all Unix-like platforms (at least those that existed around 1983).
Some details about the virus's behavior are not clear. Fred Cohen's account of the virus says that the virus infection was performed "manually by the attacker", which is a bit confusing.
Other experiments with similar viruses were planned for other platforms. Prototypes were developed for the Tops-20, VMS and VM/370. All were file viruses and all were able to gain root provileges. Further experiments were not permitted. There were also experiments on IBM PCs and Radio Shack brand computers.
Cohen's virus was only a demonstration. There is a story of him deliberately setting the virus loose on the university computers, but its truth is uncertain. If it is true, then it would likely have not caused any damage.
Cohen credits his professor Leonard Adleman with coining the term "virus". When Cohen proposed the experiment to Adleman, the professor thought, "[T]here was no point in doing the experiment," Dr. Adleman said. "It was obvious it would work." After the demonstration, Cohen and Adleman had long discussions over the ethics of the virus.
The first virus infection was on the Unix "vd" program, a program that displays Unix file structures.
Projects concerning viruses were cancelled shortly after Cohen's virus was demonstrated. The security officer at Cohen's facility was so strongly opposed to any experiments concerning security, that he would not even read any proposals.
Fred Cohen. Fred Cohen & Associates, Experiments with Computer Viruses. 1984
Gina Kolata. The New York Times, SCIENTIST AT WORK: Leonard Adleman; Hitting the High Spots Of Computer Theory. 1994.12.13