In Dragon Flyz, 41st century is an era of disappearance in Earth's mankind caused by a series of nuclear attacks led to extinction of living organisms and leaving the surface uninhabitable.
In the film A. I., which begins in the mid 22nd century, a sequence said to take place 2000 years later, features the extinction of mankind after the ocean freezes over, but the descendants of mankind's early intelligent robots, the Mechas, return to Earth and are seen excavating parts of frozen-over NYC to discover their origins and discover an ancient android, a boy named David.
The novel series Fifth Millennium by Stirling, Wehrstein and Meier is set in this time, chronicling the lives and travels of several connected characters in a 'low magic' fantasy world that emerged after a nuclear war destroyed almost all former civilization on Earth.
The Marvel Comics super-villain Kang the Conqueror rules the Earth in the 41st century according to the comics, claiming Earth was at war with weapons engineered centuries earlier when he landed in a thousand years earlier than his destination by mistake.
4010: In an episode of Justice League Unlimited, "This Little Piggy", Batman and Zatanna request an audience with Medusa in her prison in the Underworld, for information on the whereabouts of Circe, who has transformed Wonder Woman into a pig. Because of her help, Themis informs her she has earned 400 years off her sentence. Medusa's response is to sarcastically twirl her finger in the air while saying "Freedom in 4010, ring-a-ding-ding...".
The Blasterman universe mainly takes place in the early 4060s.
The events of the Doctor Who episode "42" take place in the 42nd century.
The anime Turn A Gundam takes place 2000 years after the start of the Universal Century. CC 2345, or 4390 AD.
The events of the Doctor Who episode "Planet of the Ood" take place in the 42nd century, in the year 4126. The Ood cease to be slaves to humans at this point in time, after the Doctor disconnects a force-field around the Ood-mind. Humanity spreads across three galaxies during the Second Great and Bountiful Human Empire.
The Japanese anime Battle Athletes takes place in 4999 at an athletic training school in Antarctica, which is located on the equator after a great catastrophe in 2015.
In several stories written by H. P. Lovecraft, the beginning of "the cruel Tsan-Chan Empire" will take place in the year 5000.
In the TV show Regular Show episode called "The Night Owl", Mordecai, Rigby, Mitch "Muscle Man" Sorenstein, and High Five Ghost entered a contest and when they nearly won, the host who made this contest froze them until the year 4224.
In the TV show The Simpsons episode "Bart of Darkness" they show an Itchy and Scratchy show called "planet of the Aches". This scene took place 3000 years later when it aired in 1994. And the setting is probably 4994.