Retirement was the action of ceasing to work in a professional capacity or the state of having done so.
The Doctor
The Sixth Doctor once retired. (PROSE: The Spindle of Necessity)
Following the loss of Amy Pond and Rory Williams (TV: The Angels Take Manhattan) and narrowly averting disaster after being manipulated by the Daleks, (PROSE: The Dalek Generation) the Eleventh Doctor retired from his travels to Victorian London, secluding himself in his TARDIS for a lengthy period of time. (TV: The Snowmen, The Great Detective) He eventually returned to action after being phoned by Clara Oswald. (TV: The Bells of Saint John)
Upon seeing the burnt and ruined Trenzalore, where he was fated to die, the Eleventh Doctor sardonically joked that he had hoped to one day retire and take up a quiet hobby. (TV: The Name of the Doctor) When he later visited the National Gallery, he again voiced this hope, musing that he could become the museum's curator. Immediately after, he met the Curator himself, who implied that he was a future incarnation of the Doctor. (TV: The Day of the Doctor)
The Twelfth Doctor promised Nardole to semi-retire from leaving Earth to guard the Vault at St Luke's University. Upon meeting Bill Potts though, he struggled to keep this promise. (TV: The Pilot) He eventually broke it completely. (TV: Oxygen, World Enough and Time)
The Fourteenth Doctor, at the urging of both his succeeding incarnation and Donna Noble, agreed to retire on Earth and live alongside Donna and her family following his bi-generation and the defeat of the Toymaker, in order to rehabilitate and recuperate from the emotional baggage he had been handling for years. However, the Doctor continued to have little adventures in the TARDIS with his new adoptive family during this time. (TV: The Giggle)
By one account of the Unbound Doctor's life, he eventually returned to Hong Kong and grew to enjoy his exile as a peaceful retirement. (AUDIO: The 100 Days of the Doctor)
Humans
In 1964, Rachel Jensen retired to raise begonias and write her memoirs, ending her career in her early forties. (PROSE: Remembrance of the Daleks, Who Killed Kennedy) However, she later came out of retirement. (AUDIO: Threshold)
In 1976, Alistair Gordon Lethbridge-Stewart retired from UNIT and became a mathematics teacher at Brendon Public School. (TV: Mawdryn Undead)
As the oldest-serving staff member by several centuries, Jack Harkness' Torchwood pension would be massive, should he ever retire. (AUDIO: The Torchwood Archive)
Jeremiah O'Kane retired as director of Hawthorne and left his successor, Colin Dove, with a lifetime supply of tea. (HOMEVID: The Zero Imperative)
Whittaker was headmaster of Winterborne School for decades before the governors persuaded him to retire, replacing him with the younger Gavin Purcell. (HOMEVID: The Devil of Winterborne)
Dave Cooke retired as a cleaner at Torchwood Tower and was given a cake and engraved pen by Yvonne Hartman. (AUDIO: Locker 15)
Tommy Pierce wished to retire after fifty years of working at Torchwood One. However, Yvonne told him that he had agreed to work at Torchwood for life. (AUDIO: Retirement Plan)
Anne Hartman retired from the Land Registry due to her increased workload and depression. She moved to a small cottage in Shropshire. (AUDIO: The Rockery)
Graham O'Brien was a bus driver, but had retired prior to becoming a companion of the Thirteenth Doctor. (TV: The Woman Who Fell to Earth, Rosa)
In the Unbound Universe, Alistair Gordon Lethbridge-Stewart was disgraced and removed from UNIT. Though he'd hoped to settle in New Zealand, he retired to Hong Kong and managed the Little England pub. (AUDIO: Sympathy for the Devil) By one account, the Doctor eventually returned him to Hong Kong and joined him in retirement. (AUDIO: The 100 Days of the Doctor) By another, Alistair had spent some time as the Doctor's companion and chose to retire on Skaro following the Quatch invasion, acting as a mediator for the Thals and Daleks. (AUDIO: Masters of War)
Other species
Prentice retired from adventuring to Keelmouth in 1933. (PROSE: Bide-a-Wee)