I don't know of any such drugs being known or commonly used in Classical Greece, but they may well have existed. The most famous story of Greeks tripping balls is Xenophon's account of men of the Ten Thousand eating "mad honey" on their march to the Black Sea:

The soldiers who ate of the honey all went off their heads, and suffered from vomiting and diarrhoea, and not one of them could stand up, but those who had eaten a little were like people exceedingly drunk, while those who had eaten a great deal seemed like crazy, or even, in some cases, dying men. So they lay there in great numbers as though the army had suffered a defeat, and great despondency prevailed. On the next day, however, no one had died, and at approximately the same hour as they had eaten the honey they began to come to their senses; and on the third or fourth day they got up, as if from a drugging.

-- Xen. Anabasis 4.8.20-21

In the introduction to his The Long March (2004), Robin Lane Fox theorised that the honey in question was made from the yellow-flowering rhodondendron luteum local to the region, and would have contained acetylandromedol.

The most common narcotic substance used by the Greeks was, of course, alcohol.

There has been suggestions that the oracle of Delphi inhaled naturally occurring ethylene gas (Spiller HA, Hale JR, De Boer JZ. “The Delphic oracle: a multidisciplinary defense of the gaseous vent theory”. J Toxicol Clin Toxicol. 2002 Jun;40(2):189-96.)

The Eleusinian mysteries have been speculated to involve hallucinogenic drugs, either ergot or some form of mushrooms.(http://www.maps.org/images/pdf/books/eleusis.pdf)

Opium was definitely in use on Crete. (https://www.researchgate.net/publication/223596674_Archaeological_evidence_on_the_use_of_opium_in_the_Minoan_world)

A variety of deliriant e.g. belladonna, aconite etc. were known and used for various purposes, potentially people also got high off of them.