According to the storyline of the 1982 video arcade game Robotron: 2084, in 2084 man perfects the Robotrons, a robot species so advanced that man is inferior to his own creation.
In the X-COM Storyline, the Fourth Alien War (AW-IV) starts in 2084.
Second American Civil War (2083 to 2086) in Judge Dredd
The events described by a fictional version of Evel Knievel in the Midnight Brown song 2084. Including things like the TV series "Dog Monkey vs. Monkey Dog" and streets made of syrup.
A war in Ayreon's universe is set in 2084, essentially wiping out all mankind and creating a new soul, the new Universal Migrator.
The first year of the Universal Century, the time line in which the 1979 anime series Mobile Suit Gundam and many of its sequels takes place, coincides with 2081.