Glasses
Glasses — sometimes called spectacles or specs — 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 which were just his normal glasses tinted by his sonic screwdriver while on San Helios (TV: Planet of the Dead) and upon landing in the Ood Sphere. (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)
For mind control
Another type of eyewear was used by War Lords von Weich and Smythe to implant suggestions into the minds of their human subordinates, ensuring total obedience and an escape from awkward situations, such as a human discovering a SIDRAT. The true term for these devices was not known, but they were of non-human origin. Whilst many of the Resistance retained their will against the devices, private Moor succumbed to its brainwashing, becoming convinced that von Weich was his commanding officer. Moor however finally broke free of his mental state and killed the War Lord. (TV: The War Games)
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)