OLYMPIC URBAN LEGEND: Athletes during the Ancient Greek Olympic Games were amateurs.
Until the 1970s, competition in the Olympic Games was reserved for amateur athletes, which in this sense is defined strictly as "athletes who do not get paid to perform their sport." Slowly but surely various Olympic sports relaxed their rules to allow for professionals to compete in the Olympics and today, there are few Olympic events that only allow amateurs to compete in them (boxing is a notable exception). The rules preserving the Olympics as an "amateurs only" event were quite strict during the early days of the modern Olympics.
Not only could you have never received any monetary prizes for your athletic achievements, but you would be barred (in theory, at least) for working as a sports teacher or if you had ever performed against professional athletes, even if you yourself were not paid for the event. The most famous example of this rule being enforced is Olympic legend Jim Thorpe, who had his medals from the 1912 Olympic Games revoked in 1913 because it was discovered that he had played some semi-professional baseball during the summer while in college (a fairly common practice for college athletes, although unlike Thorpe, most thought to use pseudonyms). When these rules were devised for the Olympics, it was the tradition of the Ancient Greek Olympics that were cited.
Avery Brundage, longtime President of the International Olympic Committee (IOC), once wrote, "The amateur code, coming to us from antiquity, contributed to and strengthened by the noblest aspirations of great men of each generation, embraces the highest moral laws. No philosophy, no religion, preaches loftier sentiments." Was Brundage correct? Did the amateur code come from the Ancient Greek Games? Or were its origins slightly less noble in nature?
First, the term "amateur" did not exist in the days of the Greeks. The word comes from a French derivation of a Latin word (amator, meaning "lover"). It is defined as "lover of" and in practice, it means someone who does something because they love it, not because of money. Someone who does something because of money would be a "professional."
Therefore, the term is a bit difficult to apply to sports because pretty much every notable athlete out there does, indeed, compete because of a love for the sport. If Kobe Bryant were not getting paid $25,000,000 a year to play basketball, he would still play basketball. If there were no such thing as a professional basketball league, guys like Bryant and other NBA stars would simply play basketball as amateurs. We already saw it happen in the United States before professional leagues began - people just played in amateur leagues.
So if you are going strictly by the "lover of" definition of amateur, then yes, the Ancient Greek athletes were, indeed, amateurs. However, that is not the definition people like Avery Brundage were going by when they established strict rules about monetary rewards for athletes. They were referring to the notion that getting paid for your sport means that you are not an amateur.
And here, there is no support in Olympic history. Olympic athletes during the Ancient Olympic Games were well compensated for their efforts. Victories in the Olympic Games were cause for what we would call today "bragging rights" between the various Greek city-states, and this heated competition soon resulted in increasing levels of compensation for the participants.
In 600 B.C., a winning athlete from Athens was given 500 drachma, an enormous sum - enough that he could theoretically live off of it for the rest of his life. By 200 B.C., Greek athletes had formed professional athletic guilds similar to today's Players Associations for the various professional sports. In fact, professionalism in the Olympic Games were so widespread that they even drew criticism back then from observers who noted that the financial rewards of the Games were causing young Greek men to shirk their other studies to concentrate on athletics, resulting in these men becoming worse soldiers and scholars.
So no, the idea of extolling the virtues of athletes who are not compensated for their performances was not an Ancient Greek idea. In fact, the notion was developed far more recently, in Victorian England, by men like Dr William Penny Brookes, founder of the Much Wenlock Olympian Games in 1850. Brookes' attempt to resurrect the Olympic Games inspired similar efforts, like John Hulley and Charles Melly's Liverpool Olympics in 1862 (organized with input from Brookes).