Professor Farnsworth invents a time machine that can only travel forward in time, but not back again, hopefully to avoid creating confusing and disgusting paradoxes. This causes Fry, Bender and Professor Farnsworth to be stuck in the future when the Professor accidentally turns the lever too far.
Bender keeps Fry up all night, therefore Fry oversleeps and arrives at Planet Express – around the time he is supposed to meet Leela at Elzar's Fine Cuisine for her birthday lunch. When he finally arrives, Leela has already eaten both their meals, she then leaves Fry the bill, and storms out.
Fry tries to make it up to her and tells her he will meet her for dinner at the Cavern on the Green – although this means he will miss Hedonismbot's "Girls Gone Wildest" bachelor party. Just as Fry wants to leave (on time) to meet Leela, the Professor makes him try his new one-way time machine. Fry has gotten Leela a record-a-message card, and says he'll just have to film it in the machine. They are supposed to go one minute into the future but the professor slips and they go 7000 years instead, during which Fry's card flys out the machine's window. Later that night (in the year 3010) everyone at Hedionismbot's party but him dies due to an atomic powered hooker bot meltdown. Leela, having been stood up again, thinks Bender, the Professor and Fry were at the party. She is "sad.. but still angry... is it possible to be both?"
The involuntary time-travelers try to go forward in time until they reach an era where humanity has developed a backwards time-machine. Meanwhile, in 3030, Leela misses Fry and hits on Cubert for his (perceived) similarity to Fry. Fry, Bender and the Professor, after visiting several eras in Earth's future, involving several parodies of H. G. Wells' The Time Traveller, ostrich-riding knights, a dystopian New New York, and an era of humanity enslaved by giraffes, then come to a future where robots enslave/destroy humanity and – of course – Bender immediately likes it. Fry and Farnsworth, however, are not impressed by the mountain of skulls (nor by the gorgeous view over the blood lake) and push the machine forward to a future where there are beautiful women, the few males are in high demand (even the dumb and old ones) and backwards time-travel has been developed. Bender, still angry at Fry and Farnsworth, activates the time-machine again to get even.
Forty years after Fry's 'death', Planet Express has developed into a big and successful company. Leela has found that Cubert is not really like Fry at all, and has divorced him after an affair with Cyborg-Amy. Suddenly, Fry's birthday card appears out of thin air as the time machine shoots through time, revealing that that was when it flew out the window. Leela learns that she was angry at Fry for no reason, and that while he is alive somewhere in the future (with Farnsworth and Bender), they won't meet again.
She goes to the Cavern on the Green and leaves a message for Fry by shooting holes in the ceiling. The water dripping from the holes will form stalagmites, making the message visible, and Leela hopes that perhaps at some point in the future Fry will see her message. Meanwhile, in the year 1,000,000,000, all life on Earth has become extinct. Fry finds Leela's message and seems content with his life. He suggests to skip even further forward in time and watch the end of the universe and Farnsworth and Bender assent.
After all the stars explode and the last proton decays, the group gets bored. Surprisingly a new big bang occurs and a new, identical universe is created. They watch the creation of the Sun, Earth and Moon, evolution, dinosaurs, "history" (Farnsworth also takes the opportunity to vaporize Hitler) and finally arrive back at the time they left. The Professor slips again, however, so they have to "bring her 'round again." So they take a second trip through time (this time Bender takes the controls, causing Farnsworth to miss Hitler) and on their second approach on the destination time they accidentally crush their alternative selves. Fry rushes off and makes it in time to the Cavern on the Green. As the two stand on a bridge, with Bender burying their time-paradox duplicates underneath, Fry apologizes to Leela for losing her card. She tells him that it is okay, because what she will always remember is their time together.
After ending the lives of Fry, Bender, and Professor Farnsworth from the final universe they travel to, Professor Farnsworth mentions that they have inadvertently settled a time travel paradox. It is important to note, however, that no actual paradox existed since the trio had traveled into a separate and distinct universe. Had the trio merely waited another minute in temporal flux, the alternate versions of themselves would have entered their own time machine and left on a time travelling journey of their own into the future. Also, since Fry had no interaction with Leela after going on his time journey it would not necessarily stop him from reaching the end of the universe and going around again.
It has been suggested that the reason for this universe be ten feet lower than the previous universe could be because of the presence of two additional Forwards Time Machines. However, this means that the new universe is not an exact duplicate of the original, and that would be why the previous universe's Fry, Bender and Farnsworth are capable of preventing the current universe's travel.
Another possibility also exists - that the trio had in fact skipped past one universe, having 'missed their stop' and that the trio had simply existed in one of the universes that was skipped. This would mean there is always a Fry who is traveling through the time stream of the universe and makes it to Leela's dinner a universe late, and a Fry who gets crushed.
It can be theorized that the reason the universe repeats itself during the trio's voyage is, in fact, their continued existence following their universe's collapse, even as a time-traveling anomaly, meaning their very presence affects the new universe's formation, namely in repeating the universal timeline resulting in their creation, life and circumstances leading to their flight (Hereby explaining why the universe is an exact duplicate).
Their presence may also be the actual motivation for the formation of the universe. One thesis for the universe's end involves it settling into a "dark era", or losing all heat, hereby all energy, and dying, but travelling through time in any direction requires near-infinite amounts of energy, and if the machine's energy was discharged to the dead universe, it could very well have facilitated a second big bang (Being a source of incredibly dense energy). Still, this is pure conjecture.
This episode makes Fry even more of an anomaly in time and space than he has ever been before. He was his own grandfather in the universe he was born, gifting him with a lack of a Delta Brain Wave and making his existence cyclical, and now the current Fry is living in a universe that he was not even born into, making him as a time traveller no longer subject to alterations in the time stream anywhere in the current universe. Additionally, Bender and Farnsworth are also not subject to alterations in the time stream.