The answer depends on how we interpret the question. What is a theme park?

If we're looking specifically for "something resembling water slides, slippery dips, rope swings, or anything else built solely for physical thrills," then the simple answer is no, there was nothing like this in Antiquity.

If you were an Ancient Greek looking for physical thrills, you'd go to the gymnasion (usually an enclosed field, maybe with some rooms for dressing down and oiling up) and try your hand at boxing, wrestling, throwing the javelin or the discus, running, or jumping with weights. The most daring would try to specialise in the pankration, a fighting sport that was regularly lethal. If you were rich, you might get yourself a racehorse - or nag your dad for a racehorse, which was enough of a theme in rich Athenian families for the comedian Aristophanes to make fun of it in his plays. Traditionally the most thrilling activity for the rich had been racing in two- or four-horse chariots, but by the Classical period this was generally outsourced to a sponsored charioteer for major competitions like the Olympic Games. Hunting was another classic thrill-seeking activity, and one that many authors considered good preparation for war, since it trained physical endurance and good reflexes as well as cunning and teamwork. The most common game was the hare.

Of course there were many activities that the Greeks engaged in that we would consider to be somewhere in the gray area between gambling, thrill-seeking and violent indulgence - dog-fighting and cock-fighting being the more civil varieties, raiding and piracy the more aggressive ones. Very rich Greeks of the Archaic period seem to have owned their own fifty-oared ships, which they used in the off-season of farming (May-June) to go out for raiding or trading, as the mood took them. A scene from the Odyssey, in which a recently landed ship's crew is warily asked whether they have come to raid or trade, shows that the decision could be taken on a whim. Later on, activities of this sort were mostly monopolised by the state.

During religious festivals, large parts of the territory might take on more of a "theme park" feel, with processions going from the urban centre to distant sanctuaries, and both urban and rural sanctuaries becoming the site of public offerings and feasts. The entertainment was largely in the parade, the ritual and the public meal, though certain festivals came with theatre performances of new plays (the Athenian Dionysia and Lenaia) or elaborate dance performances (f.ex. the Spartan Gymnopaideia and Hyakinthia). Since spaces like theatres and open-air altars were built for the purpose, you could argue that the Greek city itself had a significant entertainment element in it. Later on, the Romans would build their own amphitheatres (for gladiator shows etc.) as well as hippodromes for chariot races.

But we can find more interesting things if we stretch the concept of the theme park a little bit. If we interpret it not as a space with rides and physical activities, but as a purpose-built leisure area, there are many examples from the ancient world. The possibly historical Hanging Gardens of Babylon are a prime example; more reliably attested are the lavishly landscaped Persian gardens, which the Greeks called paradeisoi and from which the English language gets the word "paradise". These were walled spaces, carefully organised according to pre-drawn plans, filled with water features and rare trees, which were intended as a place of peaceful refuge for Persian nobility or as a way to seclude and beautify sacred spaces. Greeks who had seen these Persian gardens were always in awe of them, and several Greek authors lovingly described these recreational areas as an example of the power of humans to beautify their surroundings.

We also find ancient theme parks in another sense: places that redefined themselves as tourist attractions and changed local traditions to suit foreign visitors. While Roman Athens mostly continued its old traditions (like the ephebeia and the Eleusinian mysteries) as before, but simply allowed distinguished foreigners to take part in them, Roman Sparta effectively became a parody of itself in order to suit foreign tourists. They had long had a prominent ritual in which young boys tested their courage and cunning by attempting to get past older boys with whips to steal cheeses from the altar of Artemis Orthia. In the Roman period, however, the ritual became steadily more brutal, to show the Roman tourists what Spartans were supposedly like; by the 1st century BC, the ritual simply involved boys being whipped until they passed out, trying to prove that they could take it without screaming. The Spartans deliberately built audience seats around the altar so the tourists could get a good view.

In short, there were many different kinds of thrill-seeking, entertainment and relaxation available to peoples like the ancient Greeks, but nothing specifically like our modern theme parks. Those looking for physical challenges would do sports, sail boats, or go to war. Of course, the ones that had a thirst for such things would mostly be rich men; the poor had plenty of back-breaking labour to fill their days with, and were happier to be entertained with a free meal and a show than with more hard work and potential danger.

"Step right up and see it! The one and only, the superlative, the splendorous sepulcher of Ajax! You sir - yes you, with the toga and the puzzled expression! You seem to be a person of rare wit and discernment! Wouldn't you like - for the meanest mite of an entry fee - to admire the tomb of a great hero, whose exploits were described in deathless verse by Homer himself? Wait! Why are you walking away? Romanus es? Dicesne linguam Latinam? Hey!..."

OK - the classical world didn't really have carnival barkers. Nor did it have anything like the elaborate rides of modern amusement parks (though wealthy Romans sometimes paid to "ride" the rapids of Egypt's First Cataract in small canoes). There were simple rope-and-plank swings - you can see them on a few Greek vases - but nothing more sophisticated or death-defying than that. The technology wasn't there, nor the structured leisure and large middle class that make modern amusement parks profitable.

But the classical world did have what I like to think of a theme park: the city of Ilion, which claimed to be Homer's Troy. Ilion had a long history of attracting the literary equivalent of thrill-seekers. Among the first visitors was the Persian king Xerxes, who arrived at the head of the massive army he was leading against Greece. Probably as a publicity stunt aimed at the many Greeks among his soldiers and subjects, Xerxes toured Ilion, sacrificed a thousand oxen at the city’s Temple of Athena, and had his magi honor the tombs of the Trojan heroes – but not their Greek counterparts. More than a century later, Alexander the Great – who was so obsessed with the Iliad that kept a copy beneath his pillow – stopped at Ilion at the beginning of his invasion of Persia. He pointedly honored the Greek heroes buried at Troy and even ran naked to the Tomb of Achilles. Before departing, he dedicated his arms at the Temple of Athena, taking in exchange an ancient shield and armor said to date from the Trojan War. He would carry these relics all the way to India.

It was in the Roman period, however, that Ilion became a bona fide tourist attraction. Julius Caesar elevated the city's profile in the Roman imagination when he made a well-publicized visit just after defeating his great rival Pompey - partly in imitation of Alexander, and partly to advertise the fact that his family claimed descent from the Trojan hero Aeneas. Shortly before his assassination, it was even rumored that Caesar planned to re-establish Troy, and make it the new capital of the Roman Empire. Virgil's Aeneid, which gave new life and splendid literary color to the old myth of Rome's Trojan origins, ensured that Troy / Ilion remained on Roman minds.

Over the following centuries, so many tourists visited Ilion that the city began to mint coins showing Homeric heroes as souvenirs. Perhaps the most colorful visitor in this era was the emperor Caracalla, who cremated one of his courtiers on a Homeric-style funeral pyre just outside the city. Ilion’s attachment to the Trojan War tradition lasted long enough for Julian the Apostate, the last pagan emperor, to be given a thorough tour of the sights by the city’s Christian bishop.

Visitors to Ilion were shown the tombs of Achilles and Ajax (which inconveniently washed away during the reign of Hadrian), shrines for Hector and other Trojan heroes, the River Scamander (a rather unprepossessing little stream), and the sites where various famous episodes in the Iliad had occurred. If visitors were especially lucky, they might encounter the ghosts of the heroes themselves, who were said to lurk around their tombs.

There was, unfortunately, a marked absence of slippery dips and rope swings at Ilion. Even Baiae, the Roman Empire's "sin city," offered no thrills more tingly than a brisk nude swim in the Bay of Naples. In the classical world, at least, Homeric tourism was about as close as we get to theme parks.

I talk more about cultural tourism in the Roman world on this page.

(As always, I will be delighted to answer follow-up questions. Unfortunately, thanks to a severe windstorm, my whole area has been without power (and , a fortiori, internet) for the past day, so my response time might be slower than usual).

Now what about outside of Rome and Greece? Like China or the Americas?

Just to piggyback on this post: is there any evidence of physical rides in medieval times? Swings? Slides?