Drowning was a condition where an individual's lungs were filled with something other than what they normally breathed. It could eventually lead to death.
In 2269, James T. Kirk, Leonard McCoy and Carver nearly drowned when the urn constructed on Taurean urn they were hiding in filled with rain water. (TAS: "The Lorelei Signal")
Also in 2269, Spock and Kirk were saved from drowning by the Aquans and turned into water breathers. (TAS: "The Ambergris Element")
In 2358, Vice Admiral Janeway drowned under the polar ice cap on Tau Ceti Prime. (VOY: "Coda")
In 2370, Bajoran collaborator Ches'sarro Seeto was drowned in a pond on his property after Odo began questioning Vaatrik Pallra about his identity. (DS9: "Necessary Evil")
The Joranian ostrich could sometimes hold its head under water for so long that it drowned. (DS9: "Past Prologue")