Glasses were a set of lenses fitted into frames that allow for fixed, enhanced or altered sight.
The Doctor wore glasses at various points in his life — sometimes for good cause, and sometimes because, in the words of the Tenth Doctor, they made him "look a bit clever". Other people wore glasses for a variety of reasons.
The Doctor
Medical need
Only a couple of the Doctor's incarnations — the first and eleventh — actually used glasses correctively. The First Doctor sometimes wore a pair of wire-rimmed spectacles, but it wasn't known until after he regenerated that he actually required them to correct myopia.
The newly-regenerated Second Doctor briefly donned these on Vulcan to examine the murdered Examiner's badge before realising he could see perfectly well and didn't need glasses anymore. (PROSE: The Power of the Daleks)
Much later, Eleventh Doctor claimed that Amy's glasses improved his reading (TV: The Angels Take Manhattan) though they additionally served as a memento of her. (TV: The Snowmen)
Extreme long distance vision
The First Doctor carried a pair of opera glasses in his pocket. He used them for his first glimpses of the Dalek City on Skaro. (TV: The Daleks) The Ninth Doctor owned a similar pair. (TV: The Empty Child)
Cosmetic use
The Fifth Doctor typically wore a pair of glasses in times of great stress, especially following his regeneration. (TV: Castrovalva) The Tenth Doctor wore a pair of tortoise-shell rimmed square glasses, usually when he was concentrating on a particular object or subject, indicating either extreme interest or "action mode". (TV: Tooth and Claw et al) The older incarnation claimed that both these and the Fifth Doctor's half-moon glasses were not at all medically necessary but worn just because they made the two Doctors "look a bit clever". (TV: Time Crash)
Exceptional cases
The Seventh Doctor seemed to use a pair of glasses to enhance his hypnotic ability. (TV: Silver Nemesis)
The Tenth Doctor used a pair of 3D glasses when observing the effects of the Void on people and objects. (TV: Doomsday) He also wore a pair of sunglasses while on San Helios which were just his normal glasses tinted by his Sonic screwdriver (TV: Planet of the Dead) and upon landing on the Planet of the Ood. (TV: The End of Time)
The Eleventh Doctor wore a pair of thermal imaging 'sunglasses' to detect Silurians in the dark. (TV: The Hungry Earth)
Other people
As disguise
The Master often used a pair of glasses as part of a disguise, such as his disguise as Reverend Magister whilst in Devil's End. (TV: The Dæmons)
Rory Williams once wore glasses at NASA headquarters prior to the launch of Apollo 11 in order to give the appearance of being a United States government official. (TV: Day of the Moon)
Other uses
Rory also once wore a special pair of glasses which allowed the Eleventh Doctor to see everything Rory saw, through a screen in the Doctor's TARDIS, (TV: The Girl Who Waited) in a manner similar to the Eye-5 contact lenses used by Torchwood. (TV: Reset)