Drugs are certainly not a new phenomenon. Two well-known examples are opiates and cannabis. A great deal has been written about the use of hashish by medieval Nizari Ismailis (which gave us the word "assassin", derived from the Arabic "Hashshashin").
When I was studying the archaeology of Cyprus at Birkbeck in the late 1990s I wrote a paper on opiate use in the ancient Eastern Mediterranean. I've summarised many of the salient points from that paper (with a few updated links) below:
Opiates were certainly very prevalent in the Eastern Mediterranean in antiquity. The earliest written source that I know of is Hesiod's Theogony, where Prometheus is supposed to have tried to use poppy juice to drug Zeus at the city of Mekonê ("poppy town") near Corinth.
The earliest use of opiates that I'm aware of in Europe dates to the Bronze Age. On Crete, excavations of what appear to be "shrines" dating to the Minoan Post-Palace period (1,400 - 1,100BCE) have discovered figurines that Professor Spyridon Marinatos described as the "Poppy Goddess". A careful examination of the poppies confirms that they were the shape and colour of the opium poppy [S. Marinatos, 'The Minoan goddesses of Gazi', Journal of Archaeology (Greece) 1937, Vol. I, pp. 278-291].
The British Museum holds a number of small Cypriot base-ring jugs which have been dated to the Bronze Age and which are shaped like inverted poppy seed pods. This type of jug has been found in excavations across the Eastern Mediterranean. An archaeologist named Robert Merrillees suggested that the shape of the jug might have been a form of advertisement for its contents, and that the drug might have been exported across the region from Cyprus.
Residue analyses carried out on one of the jars in the British Museum collection did, in fact, detect traces of opiates which appeared to confirm Merrillees' theory. However, subsequent analyses from other jugs excavated in the region failed to detect any evidence of opiates, and it has been suggested that the confirmed case was a result of the re-use of the jar.
One note of caution though. Even if the use of opiates was fairly widespread in the Eastern Mediterranean in the Bronze age (and the evidence is inconclusive), we cannot be certain to what extent they were taken recreationally. The use of opiates for pain relief is fairly well known, but I also remember that my tutor (who was a big fan of the Minoan culture on Crete) was keen to point out that opiates can also be used as as an anti-diarrhoeal drug, and that (at that time) only one of the Cypriot poppy jugs had been found on Crete. (She also pointed out that the Minoan sites on Crete and Santorini appear to have had toilets connected to sewers with running water to dispose of the waste, and invited us to draw our own conclusions). However, if the drug was widely available, then it is hard to believe that it wouldn't have been taken recreationally.
EDIT: While doing a little further research on the subject, I just found this paper from the UN Office on Drugs and Crime which covers the use of poppies and opiates in the ancient Eastern Mediterranean. Hope this is useful.
The final part of your question, asked whether any ancient kingdoms (not including the Chinese opium wars) had problems with the citizens abusing drugs?
In the Islamic world, alcohol was (and is) prohibited under Sharia law. This is often interpreted as prohibiting all intoxicants (not only alcohol). Despite that, the practice of hashish smoking seems to have continued throughout the history of Islam (against varying degrees of resistance at different times and in different places).
Apart from the prohibition under Islamic Sharia law, I'm not aware of any legal prohibitions against recreational drug use in the ancient or medieval periods in Europe or the eastern Mediterranean. This suggests that, if there was a problem with recreational drug use at these periods, it wasn't considered to be serious enough to require legislation.
Hopefully others can add answers which cover other recreational drugs in other geographic regions in the ancient and medieval world.