Glasses were a form of eyewear, an early way of correcting vision for those with eye problems. They were replaced by either corrective laser surgery, or special kinds of drugs and treatments developed through the study of medicine.
Glasses were worn by some in the 23rd century. A transporter assistant serving aboard the USS Enterprise in 2254 wore glasses while working at the transporter console. (TOS: "The Cage", "The Menagerie, Part I", "The Menagerie, Part II")
Crime lord Bela Okmyx of the planet Sigma Iotia II wore glasses. (TOS: "A Piece of the Action")
A command division lieutenant of the USS Enterprise who beamed down to the Terratin city on Terra 10 also wore glasses. (TAS: "The Terratin Incident")
Captain James T. Kirk was allergic to Retinax V, the conventional pharmaceutical method of correcting vision, so Dr. Leonard McCoy provided him with a pair of 18th century glasses on his birthday. However, the glasses broke during the conflict with Khan Noonien Singh and his followers. (Star Trek II: The Wrath of Khan) Kirk ended up selling the glasses at an antique shop on 20th century Earth in exchange for currency needed to accomplish their mission to save Earth in the future. When Spock expressed his surprise that Kirk would sell a birthday present from a friend, Kirk assured him that somehow he'd still wind up with them anyway. (Star Trek IV: The Voyage Home)
Glasses were also common on Malcor III. Both Krola and Lanel wore them. (TNG: "First Contact")
In 2368, several artifacts were recovered from a cavern underneath the Earth city of San Francisco. Among them was a pair of glasses which Lieutenant Commander Data described as a "bifocal visual aid." (TNG: "Time's Arrow")
In the holographic program titled Julian Bashir, Secret Agent, the character Honey Bare wore glasses, but Doctor Julian Bashir convinced her to take them off. (DS9: "Our Man Bashir")
In visions received from the Prophets, Benjamin Sisko's 20th century persona Benny Russell wore glasses. (DS9: "Far Beyond the Stars")
In 3189, Kovich wore glasses, as he believed they made him appear more intelligent. (DIS: "Die Trying")
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Background information
In a deleted scene in Star Trek: Insurrection, a librarian serving on the USS Enterprise-E (played by Lee Arnone-Briggs) wore glasses.