It is generally believed that the first computer virus to be unleashed on vulnerable computers was the Creeper Virus. The Creeper Virus infected the forerunner to the internet, a computer network called ARPANET. This was back in the early 1970s. The virus was non malicious in that it did not harm the computers it affected, however on infected machines it displayed the message 'I'M THE CREEPER : CATCH ME IF YOU CAN.'
The Creeper was duly caught by what is undoubtedly the first piece of antivirus software ever created. This programme was called the Reaper (as in Grim Reaper) and it sought out computers infected with the Creeper and duly destroyed it. The Reaper programme was not like the anti-virus programs we know today, but in fact was a virus itself in that it was self replicating and spread through a network. (About a year ago we discovered biological viruses that can infect other biological viruses.)
There are a great many rumours concerning the authors of both The Creeper and The Reaper, and many suspect that it was the same person. His (or her) motivations have been analysed as possibly a joke, a scientific experiment that got out of hand, and even blackmail. Whoever it was managed to keep it away from the general public, which is remarkable in itself.
An alternative possibility is that it was not done by one person. There was considerable military involvement in the ARPANET network and one aspect of the research into ARPANET was to examine whether the system was sufficiently robust to withstand a nuclear war and still provide a communications network. Both The Creeper and The Reaper could have been military experiments to test network vulnerability and protection. This would certainly explain why the identity of the creator has never leaked out.
Ever since that first battle between virus and virus destroyer there has been a continual war waged between an ever increasing army of viruses and ever more sophisticated antivirus software. There are so many viruses and other malware lurking in hidden corners of the internet that to run a computer without adequate protection would be foolhardy.