A hangover was a feeling of malaise, often experienced after the consumption of alcohol or other narcotics. Symptoms included headache, nausea, dizziness, and sensitivity to sound and/or light.
In 2063, shortly before the launch of the Phoenix, Zefram Cochrane suffered from a "four-alarm hangover" either due to whiskey or to being stunned by a phaser fired by William T. Riker. (Star Trek: First Contact)
In 2154, Jonathan Archer described the aftereffects of his mind meld with Syrran as a "mind-meld hangover"; T'Pol told him she wouldn't call it such, but essentially he was correct. (ENT: "Awakening")
In 2269, after the effects of love potion crystals wore off, Montgomery Scott and M'Ress both suffered from hangovers. He described his hangover as shaming all other hangovers, while she asked him not to speak so loudly. (TAS: "Mudd's Passion")
In 2371, after Fred Noonan was hit by an energy weapon, The Doctor treated him and assured him he would only suffer from a hangover. (VOY: "The 37's")
In 2374, when a group of Klingon holograms awakened after passing out due to alcohol, The Doctor told Neelix since he didn't have a cure for Klingon hangovers, he couldn't help him dealing with the Klingons. (VOY: "The Killing Game")
In 2375, Norvo Tigan suffered from a hangover after talking with his sister and subsequent drinking. (DS9: "Prodigal Daughter")
The same year, Tomin had a hangover and complained that the doors aboard the USS Voyager were too loud. (VOY: "Someone to Watch Over Me")
In 2379, Worf suffered from a hangover during the wedding of William T. Riker and Deanna Troi due to having consumed large amounts of Romulan ale. (Star Trek Nemesis)
In 2401, Raffi woke up with a hangover after Sneed drugged her with Splinter. (PIC: "Seventeen Seconds")