Romulan ale was a highly intoxicating alcoholic beverage of Romulan origin with a characteristic blue color (this could range from a pale sky blue to a dark midnight blue, depending on the "vintage"). It took a while to ferment and was also used for medicinal purposes. (Star Trek II: The Wrath of Khan)
Although it was illegal in the Federation from at least the early 2280s to the late 2370s, in actual practice many Starfleet officers had sampled it at one point or another. A rare exception was Admiral William Ross. (Star Trek II: The Wrath of Khan; Star Trek VI: The Undiscovered Country; Star Trek Nemesis; DS9: "Inter Arma Enim Silent Leges")
Captain James T. Kirk was able to procure some for his crew, and served it at a state dinner with Gorkon in 2293. When pressed by one of the Klingons on its illegality, he wryly noted it was, "one of the advantages of being a thousand light years from Federation headquarters." However, the ensuing hangover convinced him to order that the drink no longer be served at diplomatic functions. (Star Trek VI: The Undiscovered Country)
In 2366, the replicators aboard the USS Enterprise-D were not capable of replicating Romulan ale; it would have required programming the devices with the molecular structure of the beverage. The recipe was not readily available due to the lack of communication and information between the Federation and the Romulan Empire. (TNG: "The Defector")
Romulan ale was even a challenge for species as stout as the Klingons, who were usually quite resistant to the effects of alcohol. After drinking a sizable amount of Romulan ale in celebration of William T. Riker and Deanna Troi's wedding in 2379, Worf, obviously suffering its effects, stated that "Romulan ale should be illegal", to which Geordi La Forge replied, "It is." (Star Trek Nemesis)
Romulan ale briefly became legal in the Federation during the Dominion War when the embargo was lifted due to the alliance between the Federation and the Romulans. However, by 2379, Romulan ale was prohibited again. (DS9: "Inter Arma Enim Silent Leges"; Star Trek Nemesis)
Blue beverages were also seen in Romulan contexts in TOS: "The Enterprise Incident" and DS9: "In the Pale Moonlight". In the latter episode, the blue beverage is identified as kali-fal, which may be the Romulan name for "Romulan ale" - they both appear to be bluish liquids that pack a wallop. However, Kali-fal is known to have a potent aroma. Romulan Ale was never mentioned to have such an aroma.
The Las Vegas Star Trek Experience sold bottles and six-packs of "Romulan ale", a blue lager-style beer made by Central American brewery Cerveceria La Constancia on exclusive license from Paramount Pictures. The Klingon actors were scripted to claim that "you humans cannot hold your neurotoxins!"
In real life there are some who have made their own "Romulan ale", for instance a mixture of Bacardi rum, Everclear alcohol, and Blue Curaçao liqueur, at equal amounts with no diluting liquid (rated at 134-proof). Another known mix is Blue Curaçao, Creme de Banana, and cream soda or ginger ale.
Romulan ale has always appeared some tint of blue, except in Star Trek Nemesis, when it appeared brownish-colored. This is either a continuity violation or an introduction of a new type of ale not seen on-screen before.
Romulan ale appears to occupy a status in the Federation similar to Cuban cigars in the United States.