Officially, in 1988 the International Olympic Committee voted to allow professionals in all sports to compete subject to the approval of the international governing body of the sport in question (http://usatoday30.usatoday.com/olympics/owg98/osytr01.htm).

In practice professionals had been competing almost since the beginning, with varying degrees of controversy. Jim Thorpe, for instance, was stripped of his medals won in the 1912 games after it was discovered he had played semi-professional sports prior to competing. These medals were restored in the early 1980's (too late for Jim, who was already dead). On the converse, many eastern bloc athletes competing post World War Two were "professional" in all but name, being paid by their governments to focus exclusively on the sport they played (http://www.coubertin.ch/pdf/schantz.pdf). This led to quite a bit of (understandable) grumbling from athletes from other countries, and helped spur the change in rules regarding amateurism. These rules grew out of the idea of sporting competition being a gentleman's pursuit, but as things changed over the course of the 20th century and sport moved beyond being the province of the upper, leisure class this idea became outdated. Hope this helps, cheers.