Why: I have extremely high standards for a time travel story. Internal logic matters more than anything. It can't involve Sandra Bullock watching a tree grow like mad or a prisoner seeing Ashton Kutcher spontaneously stigmatize or any encounter between the Fonz and a brontosaur. But X-Men writer Chris Claremont and artist John Byrne took temporal continuity seriously when they envisioned comics' scariest future. In 2013, North America is ground under the metal heels of the robot Sentinels, who have killed most of the superpowered beings and enslaved the humans. The rest of the world plans to nuke North America, which seven remaining superbeings—Sprite, her husband Colossus, Wolverine, Storm, Magneto, Franklin Richards, and Rachel, daughter of the deceased Cyclops and Jean Grey—hatch a desperate plan to deter. The psychic Rachel sends Sprite's mind back through time to stop the event that unleashed the Sentinels: the assassination of mutant-hating Senator Robert Kelly by the Brotherhood of Evil Mutants on October 31, 1980. Sprite awakens inside her youthful body, and leads the X-Men in battle against the Brotherhood on the floor of the U.S. Senate. Meanwhile, in the future, the surviving mutants attack the Sentinels in their Baxter Building headquarters. One by one... okay, there might be a clue of what happens on issue #142's cover. Is it enough to change the future? Only time will tell.
Impact: This riveting storyline jammed a stake in the earth and said, "Take comics seriously." At that time, it wasn't common for good guys to die in Marvel's comics. But just three issues earlier, Claremont and Byrne killed off Jean Grey in the most shocking comics death since Gwen Stacy. With "The Dark Phoenix Saga" and "Days of Future Past," the two laid a strong claim to the greatest writer-artist run on an ongoing mainstream comic. This run was commemorated some years later when the first X-Men film was based on "Days of Future Past" (minus the time travel), the third was based on "The Dark Phoenix Saga," and the second... well, that's a column for another day.
Personal Connection: "Days of Future Past" was the first X-Men comic I bought. Until then, I was solely a DC reader, amassing quite a collection of Batman titles. But the cover of X-Men #141 leapt off the rack at Golden Age Comics and told the 13-year-old me, "Kid, you're an X-Men fan." How could it not? Now widely acclaimed as the one of the greatest covers ever, the startling image of Wolverine and Kate Pryde spotlit in front of a superheroic body-count poster has been revised and parodied multiple times since. But you never forget your first genocide of mutantkind.
Other Contenders: that X-Men storyline's spiritual godchildren, the first and second films in the Terminator franchise; Slaughterhouse-Five, Kurt Vonnegut Jr's novel about a man who becomes unstuck in time, but doesn't mind much; "The City on the Edge of Forever" and Star Trek IV: The Voyage Home, showing the range of Star Trek's greatness; the spine-tingling Doctor Who episode "Blink", which will forever change your opinion about looking at statues of angels; Donnie Darko, a glimpse through the lookingglass; Groundhog Day, a holiday in Hell, Pennsylvania; 12 Monkeys, in which science isn't an exact science; Peabody's Improbable History, the timeless adventures of a dog and his boy.