Spanning a 1.000 years the most famous pan hellenistic games were held at Olympia starting around 700 BCE and ending in 393 CE. Considering that Greece became part of the Roman Empire around 150 BCE, the games were not just a Greek tradition, but also a Roman one. The Roman Emperor Nero participated himself and you can find the ruins of his house at the site. It was also a Roman Emperor who ended the tradition, Theodosius I, the last Emperor of both the Western and Eastern Roman Empire and of Theodosian Wall fame. The end came due to the ascendance of Christianity and the banning of pagan traditions.
What you find nowadays is a large archeological site with a focus on sports. There is the stadium and entering it via the gate has a special feel to it. There are plenty of houses for the athletes. But to me the true highlight is not sports related, it's the ruins of the Zeus Temple of Olympia. The Zeus statue that is housed was one of the Seven Wonders of the World. Supposedly, it was lost in Constantinople in a fire in 475 CE. The workshop of the famous sculptor Phidias who created the Zeus status is nearby.
Similar games were held in other Greek cities, most notably Delphi. Interestingly, Olympia also had an oracle, so there is an overlap between these two sites. Still, both sites feel different and are great additions to the list.
Last but not least, it must be stressed that Olympia (again like Delphi) has a great, not to be missed museum with great sculptures on display.
Getting There
The hub for Olympia is Pyrgos with bus connections to Patras, Kalamata, Tripoli/Corinth and Athens. From Pyrgos you can board a local bus to Olympia. There is also a functioning railway line between Pyrgos and Olympia. I am hard pressed to understand the rationale or business case for the train as it runs only a few times a day and there are no connections anywhere else.
While You Are There
I stayed overnight in Pyrgos. It's a non eventful city and there is little reason to stick around. Only noticeable benefit is that you are some 6km from a rather nice beach. The beach seems to attract mostly local visitors and therefore has little tourist amenities; I didn't even manage to buy a sunset beer. Having to kill some time, I walked there from the city.
The other WHS on the western coast of the Peloponnese is Bassae. You can read my review on how to get there. A return cab from Pyrgos should be 100 EUR.