How prevalent were recreational drugs in the ancient world?

Ancient Greece (among other cultures) are said to have used magic mushrooms in rituals and religious events, for example in the Eleusinian Mysteries

Psychoactive mushrooms are another candidate. Terence McKenna speculated that the mysteries were focused around a variety of Psilocybe. Other entheogenic fungi, such as Amanita muscaria, have also been suggested.[72] A recent hypothesis suggests that the ancient Egyptians cultivated Psilocybe cubensis on barley and associated it with the deity Osiris.[73]

There have been numerous other books and articles published on this topic.

Not sure if you are asking solely about Europe and the classical world, but the New World people and empires used drugs in a sense that might today be called recreational, but probably more accurately should be called religious or religio-political. Consumption of hallucinogenic plants and animals were part of specific ceremonies, sometimes political rituals, and not just time-killing entertainment or the like :

Hallucinogenic drugs in pre-Columbian Mesoamerican cultures. [Article in English, Spanish] Carod-Artal FJ1. Author information Abstract INTRODUCTION:

The American continent is very rich in psychoactive plants and fungi, and many pre-Columbian Mesoamerican cultures used them for magical, therapeutic and religious purposes. OBJECTIVES:

The archaeological, ethno-historical and ethnographic evidence of the use of hallucinogenic substances in Mesoamerica is reviewed. RESULTS:

Hallucinogenic cactus, plants and mushrooms were used to induce altered states of consciousness in healing rituals and religious ceremonies. The Maya drank balché (a mixture of honey and extracts of Lonchocarpus) in group ceremonies to achieve intoxication. Ritual enemas and other psychoactive substances were also used to induce states of trance. Olmec, Zapotec, Maya and Aztec used peyote, hallucinogenic mushrooms (teonanacatl: Psilocybe spp) and the seeds of ololiuhqui (Turbina corymbosa), that contain mescaline, psilocybin and lysergic acid amide, respectively. The skin of the toad Bufo spp contains bufotoxins with hallucinogenic properties, and was used since the Olmec period. Jimson weed (Datura stramonium), wild tobacco (Nicotiana rustica), water lily (Nymphaea ampla) and Salvia divinorum were used for their psychoactive effects. Mushroom stones dating from 3000 BC have been found in ritual contexts in Mesoamerica. Archaeological evidence of peyote use dates back to over 5000 years. Several chroniclers, mainly Fray Bernardino de Sahagún, described their effects in the sixteenth century. CONCLUSIONS:

The use of psychoactive substances was common in pre-Columbian Mesoamerican societies. Today, local shamans and healers still use them in ritual ceremonies in Mesoamerica.

https://www.ncbi.nlm.nih.gov/pubmed/21893367

The Aztecs consumed magic mushrooms ritually:

Called "Teonanácatl" in Nahuatl (literally "god mushroom"—compound of the words teo(tl) (god) and nanácatl (mushroom))—the Psilocybe genus of mushroom has a long history of use within Mesoamerica. The members of the Aztec upper class would often take teonanácatl at festivals and other large gatherings. According to Fernando Alvarado Tezozomoc, it was often a difficult task to procure mushrooms. They were quite costly as well as very difficult to locate, requiring all-night searches.

Both Fray Bernardino de Sahagún and Fray Toribio de Benavente Motolinia describe the use of the mushrooms. The Aztecs would drink chocolate and eat the mushrooms with honey. Those partaking in the mushroom ceremonies would fast before ingesting the sacrament. The act of taking mushrooms is known as monanacahuia, meaning to "mushroom oneself".

"At the very first, mushrooms had been served... They ate no more food; they only drank chocolate during the night. And they ate the mushrooms with honey. When the mushrooms took effect on them, then they danced, then they wept. But some, while still in command of their senses, entered and sat there by the house on their seats; they did no more, but only sat there nodding."

https://en.wikipedia.org/wiki/Aztec_use_of_entheogens#Mushrooms

Inca sacraficial children were given copious amounts of coca and alcohol prior to their deaths:

Three Inca mummies found near the lofty summit of Volcán Llullaillaco in Argentina were so well preserved that they put a human face on the ancient ritual of capacocha—which ended with their sacrifice.

Now the bodies of 13-year-old Llullaillaco Maiden and her younger companions Llullaillaco Boy and Lightning Girl have revealed that mind-altering substances played a part in their deaths and during the year-long series of ceremonial processes that prepared them for their final hours.

Under biochemical analysis, the Maiden's hair yielded a record of what she ate and drank during the last two years of her life. This evidence seems to support historical accounts of a few selected children taking part in a year of sacred ceremonies—marked in their hair by changes in food, coca, and alcohol consumption—that would ultimately lead to their sacrifice. (Related: "Lofty Ambitions of the Inca.")

In Inca religious ideology, the authors note, coca and alcohol could induce altered states associated with the sacred. But the substances likely played a more pragmatic role as well, disorienting and sedating the young victims on the high mountainside to make them more accepting of their own grim fates.

http://news.nationalgeographic.com/news/2013/07/130729-inca-mummy-maiden-sacrifice-coca-alcohol-drug-mountain-andes-children/

And finally, of course, it should be noted that the Andean people have chewed coca leaves for thousands of years as a stimulate, much like people use caffeine today, to assuage hunger, aid focus, forestay weariness, etc.

The number one recreational drug in history is ethanol. Commonly served as beer or fermented fruit juice.

It is and was cheap and easy to make, and has destroyed lives in all of recorded history.

It has also been seen as the very definition of a good party in most of recorded history. (E.g. the story in the Bible of turning water into wine)

I think one of the largest problems you are going to have is the term "recreational drugs". That term is by and large a new term. People and civilizations from back then would not have categorized drug usage in that manner.

Let me give you a good example, though much closer to modern day than you mean. Cocaine was a common pain reliever, sold over the counter at nearly any general store in the 1800s and early 1900s. People used it, and some people got addicted. But the people that used it "too much" weren't labeled as recreational drug users.

The same is true with other "recreational drugs". Peyote, pot, opiates, and the like could all be used for recreational use, but all had significant "real" uses.

Another example might be laudanum. While it had many medical uses, it could be overused. The people that overused it, though, were generally not labeled as "recreational", but instead as mentally ill, or unstable.

The point is this: "recreational drugs" is a new term meant to signify that a drug has no other use than "fun". Every one of the "traditional" drugs actually had a real legit medical or religious use. The people that abused those drugs or used them incorrectly fell into two categories (this is more modern, of course, where we have writings to go by):

1. Someone that had a good time that one time.
2. Someone that is unstable and needs care.

Only very recently have we really started to target "recreational drug" and "recreational drug usage".

So to answer your question, there are civilizations, both old and new, that use intoxicants of one kind or another for various reasons. A really common example would be ancient Egypt and their "heqet" (beer), which was used as both "control" and a staple food. But, no ancient civilization really labeled its drug usage as "recreational". That's a totally new concept.

The ancient civilizations saw overuse of drugs as a problem, from time to time, but generally "cured it" by treating the problem (sometimes very harshly). It wasn't till about the 20th century that we shifted our thinking into this idea that drug usage was a moral issue, and not a "medical" one. With that came the idea that drug usage could be "recreational". Before that, drug usage was either just fun, with a purpose, or a sign that someone was sick.

You can see some examples of ancient drugs at http://www.ancient-origins.net/opinion-guest-authors/drugs-ancient-cultures-history-drug-use-and-effects-006051

Clarification: I do not mean to say that there are no instances of people abusing drugs throughout history. Just that the people that would have done so either did it infrequently enough that it wasn't an issue, or did it so much that it was an issue. If it were an issue, then the person was sick, or unstable.