La Forge wearing sun glasses
(covers information from several alternate timelines)
Eyewear was a category of devices worn over a person's eyes. They could serve to either protect the eyes from the elements or to aid a person's vision.
Protective eyewear
Sunglasses
Tucker and Archer wearing sunglasses
Sunglasses were a form of eyewear worn by individuals to protect their eyes from a sun's rays. Captain Jonathan Archer wore sunglasses (as well as a hat, which also served to protect the eyes) during his venture into the Vulcan's Forge with T'Pol. He offered his glasses to T'Pol so she, too, would have some protection from the effects of Vulcan's suns. She refused them, however, stating that her inner eyelid would suit her needs. (ENT: "The Forge")
Several Humans at Gilgo Beach wore sunglasses in 2354 when Benjamin Sisko met his future wife Jennifer there. (DS9: "Emissary")
Beverly Crusher and Guinan wore sunglasses in the Dixon Hill holonovel. (TNG: "The Big Goodbye", "Clues")
While stranded in 2063, Geordi La Forge wore sunglasses to hide his eyes from the local residents. (Star Trek: First Contact)
In 2259 of the alternate reality, a San Francisco resident wore a pair of dark glasses while watching the USS Vengeance's attack. (Star Trek Into Darkness)
Reginald Barclay wearing two sets of sunglasses
While on a beach somewhere on Earth to meet up with Deanna Troi in 2377, Reginald Barclay wore a pair of sunglasses with an second pair of protective lenses attached to them to give his eyes additional protection from the sun. (VOY: "Inside Man")
Although Vulcan inner eyelids should have been more than sufficient to protect her eyes under Earth's sun, Commodore Oh wore sunglasses when she interrogated Agnes Jurati outside the Daystrom Institute in Okinawa, in 2399. (PIC: "The End is the Beginning")
Visor
The visor was a protective eyewear worn in the presence of Medusans. (TOS: "Is There in Truth No Beauty?")
Vision aids
3D glasses
3D glasses were worn to enable people to see three-dimensional movies. (VOY: "Repression")
Reading glasses
Reading glasses were eyewear worn to enhance a person's view of objects up close. (Star Trek II: The Wrath of Khan)
VISOR
The VISOR was a device worn by some blind personnel, such as Geordi La Forge, to enable them to see. It allowed vision over a wider section of the EM spectrum than normal vision, but many found the extra information difficult to interpret. (TNG: "Encounter at Farpoint"; Star Trek: The Next Generation; Star Trek Generations; Star Trek: First Contact; Star Trek: Insurrection; Star Trek Nemesis)