Lately, I've been comparing how futuristic-set TV shows and movies have evolved over time, and while doing so, I became curious about the following…
What's the furthest-forward-in-time time period that's ever been depicted, in either a TV show or movie?
More of an adjunct to the existing answers - if you're looking for an example where the "usual" setting of the movie or show is far in the future (as opposed to a specific episode or segment) then I'd suggest Red Dwarf as the bulk of the show is set over 3 million years in the future.
In Futurama episode "The Late Philip J Fry", some of the crew travel to the very end of time itself (and back around again... TWICE).
They most likely go through the heat death of the universe which is on the order of 10100 years!
However, the furthest "known" date shown on the time machine's indicator is 1 × 1040 AD: when the "last proton should be decaying".
It's Milliways, the Restaurant at the End of the Universe as depicted in The Hitchhiker's Guide to the Galaxy
Referenced in the 2005 Movie, and makes an appearance in episode 5 the 1981 TV series
YouTube of Arthur Dent eating here.
Milliways, also known as The Restaurant at the End of the Universe, can only be visited practically by time travel, as it exists at the end of time and matter. Marvin the Paranoid Android is one character who manages to reach Milliways without the use of time travel, merely by being very patient. One of the restaurant's major attractions is that diners can watch the entire universe end in a Gnab Gib from the windows of the restaurant as they eat. The terminal moment is followed by dessert. Reservations are easily obtained, since they can be booked once the patron returns to his or her original time after their meal, and the restaurant's bill can be paid by depositing a penny in any bank account of the present time: by the end of the universe, the compound interest on that penny over the course of time after 170 quintillion years (short scale) will be enough to pay the extremely high bill. Near-instant transportation to the restaurant can be achieved in certain rarefied circumstances, such as being next to an exploding hyperspatial field generator on the planet where Milliways will eventually be built several billion years after the explosion occurs.
I'm pretty sure you can't get further into the future than this, since you eat dessert after the end of the universe. There's probably coffee and petit-fours after that.
You can't beat the end of time answer also be matched by any number of other movies/shows like Dr Who in the year 100,000,000,000,000 5 minutes before the heat death of the universe?
The Doctor Who Episode Utopia is set in the Year 100 Trillion, at literally the very end of time and space itself (according to the show)
Adaptations of "The Time Machine" (H. G. Wells). At least two of them (1960 and 2002) depict quite detailed the year 802,701.
And in the 2002 adaptation, there are also landscapes of the year 635 427 810. It is more than six hundred million years from now.
A many-way tie!
The time for this tie is "the end of time," also sometimes portrayed as "outside of time."
There are multiple movies and TV shows, as well as literature and video games, which depict things such as the end of time, the next universe after the end of time and then time restarts, post-time time has run out and now we are in a timeless 'place' where time is some singularity or nonexistent or other weird thing, and other variations of this theme.
All of these have in common that they are at the farthest extent of time or even beyond time, therefore they all tie for first place for this answer and none of them can be beaten.
Some examples have already been given: Hitchhiker's Guide to the Galaxy, Dr. Who, and Futurama.
In "Red Dwarf" season 5, episode 2 "The Inquisitor" the crew encounter an android who has lived to "the end of time." Once at the end of time, the android decides that there are no gods or afterlife, so the android builds a time machine and goes back to the past.
Another one is the TV series 12 Monkeys. 12 Monkeys had a cult which worshipped The Witness, a person who was born outside of time by two time travelers. Two time travelers conceived the child while in a temporary "pocket timeline," for lack of a better term, which was the result of their tampering with history and which should not have happened but did due to the many accumulating paradoxes. The traveler is worshipped as the one who lives outside time and who will bring an end to time. Although "outside time" does not always necessarily mean "after time," in this case the "outside time" quality is brought about through actions taken throughout history and it brings an end to time, so it is effectively "after all time."
There are also time-travel movies and shows in which people are trying to stop "the end of time" from becoming reality, but which I do not know enough about to know if anyone actually "goes there." Example: Quantum Break
These go beyond the scope of this question but are likely of interest to most people asking this question or reading it.
There are a lot of contenders if you were to include other story media such as literature and video games...
There was a video game, Chrono Trigger I think, in which you had to travel back and forth through time as part of the plot, with the farthest time being a place at "The End of Time" which used the concept "All time is spent and this is now a 'timeless' post-time place. Time is essentially frozen in place, though you can still move, talk, and perform other actions."
And there was a choose your own adventure book which involved a time-travel cave (go in one time, come out another exit at another time) which had a special "post-time" room as well which worked the same way.
In "The Time Traveler's Almanac" one of the time-traveling short stories had time-travel technology invented, and there was also an "end of time" there, but most people avoided it because nobody ever returned from it, so its properties are unknown to those in "normal time." Sorry, I do not recall the title of this short story.
In Dungeons and Dragons there is an elf-like race called the Le Shay. In at least the 3rd edition of D&D (not sure about other editions), the description of the immortal Le Shay suggests that they are already in such a situation relative to their home-time. Due to tampering with the universe, which produced a catastrophe that could not be fixed, the Le Shay managed to, somehow (they are secretive, so this part is unknown), get themselves beyond the end of time and into the next instance of a habitable timeline. So, if those rumors are to be believed, then the default setting is a "future" timeline that is beyond the end of time of a previous timeline. Also, D&D is available as movies and TV shows, however I am not aware if the Le Shay have made any appearances on the screen - I am only aware of their existence in literature, hence mentioning this in the special notes section.
The Babylon 5 Season 4 finale, The Deconstruction of Falling Stars, is broken into a number of segments showing events affecting the Interstellar Alliance at different stages in its future. The final segment is set one million years into the future and shows
the destruction of the Earth by the Sun going nova.
The Doctor Who episode The End of the World is set in the year 5 billion.
Of all the movies and TV shows ever made, which of them **is set furthest in the future**?- or as in the question text,What's the most futuristic time period that's ever **been depicted**, in either a TV show or movie?. They are actually quite different questions.