The Late Philip J. Fry
Bender keeps Fry up all night while cavorting with his robot girlfriend, so Fry is late for work... and subsequently late for his birthday lunch with Leela. He begs for a chance to make it up to her: he'll take her for a fancy birthday dinner, and swears that he'll be there. Bender invites Fry to a "girls gone wild" bachelor party for Hedonismbot. Fry declines, telling Leela: "I can throw up on a stripper anytime. Tonight, I wanna not throw up... on you." Bender invites the Professor instead. Fry buys Leela a "record your own message" card, onto which he can record a video greeting. If he leaves for the restaurant now, he'll be exactly on time.
The Professor, however, demands that Fry and Bender help test his new time machine ⎯ which only travels into the future ⎯ by going on a test flight one minute into the future. Fry begins recording his message, but the Professor slips, and hits the take-off lever way too hard. Fry drops the card, and it flies out the open window of the now-in-motion time machine. By the time they manage to stop it, just moments later (relatively speaking), it's the year 10,000 AD, and the city is in ruins. Not only has humanity fallen, but also societies of apes, birds, cows, and some sort of slug things.
Back in 3010, Leela waits for Fry at the fancy Cavern on the Green, formed by erosion over millions of years by water dripping from the ceiling. She returns to Planet Express, irate and assuming that Fry went to the bachelor party… only to see a news report that the party ended with a nuclear-powered robot stripper going into meltdown and detonating, killing everybody there except for Hedonismbot himself. Leela is conflicted, both angry at and sad for Fry. In the year 10,000, Fry is sad that he'll never see Leela again. The Professor has an idea: they can go forward in time until the backwards-time machine is invented, and then they can go home. They visit the hostile ice age of 105,105, the medieval year 252,525, the aquatic year 351,120, and the year 1,000,000 1/2 (in which humankind is enslaved by giraffes), to no avail.
In 3030, Planet Express has become a thriving success in the 20 years since Leela seized control. She misses Fry, however... and comes on to 20-something Cubert, whose red hair reminds her of him. Meanwhile, the time machine arrives in the year five million, a world in which humanity has diverged into super-advanced creatures and hulking brutes who live underground. They haven't invented a backwards-time machine, but are sure their superior minds can create one within five years. They hop five years ahead... and find the highly evolved humans being slaughtered by the brutes.
They jump to the year ten million, in which the machines have rebelled and want to kill all the humans. Bender wants to stay, and is irate when the Professor takes off. They jump to the year fifty million, an Eden populated by super-intelligent, sexy, scantily-clad women facing a shortage of men. They've invented a backwards-time machine, and will gladly share the technology after the fertility banquet. Bender, upset that they'll stay in the future they like but not the one he likes, grabs the lever and launches them into the future once more. They arrive in the year one billion... in which all life on Earth is extinct, and the land is barren, dry, and hot. This is the end of all things; there's no point to going any further ahead. Fry, dejected, goes for a walk... and finds the remains of the Cavern on the Green. Inside, he's shocked to find a message carved into the floor. It begins, "Dear Fry..."
In the year 3050, Leela has just divorced Cubert, not really understanding why she ever married him. As she tells Hermes (now just a head in a jar) that she's resigned to being alone and is married to her job, there is a time-machine shaped shimmering in the air... and Fry's video-greeting card falls out. She watches the message, and is saddened to find she's spent her whole life angry at Fry for something that wasn't his fault. She visits the long-since-closed Cavern on the Green, and fires her blaster at the roof, carving a message. Water slowly, slowly begins to drip. A billion years later, a message is eroded into the floor for Fry to find: "Dear Fry, our time together was short, but it was the best time of my life. Leela."
Fry weeps, and then returns to the Professor and Bender at the time machine. He says he's had a good life... so what say they get back in the time machine and watch the universe end? They agree. They watch the sun go supernova and burn up the Earth, and then watch the stars slowly go out. The last proton decays. Now what? They're bored for a moment... but then, suddenly, there's a second Big Bang! Unbelievably, the new universe is exactly identical to the old one! They just need to keep going forward in time to the exact point they left. As they approach their own time, the Professor slips, and they end up in the year 10,000 again. They go around another time, this time with Bender driving. They land just a moment before this universe's Fry, Bender and Professor are going to get into the time machine. This third universe is about ten feet lower than the old one, so the time machine appears over the doubles... and falls on and kills them: thus, says the Professor, taking care of the time-travel paradox.
Fry rushes to his dinner with Leela, apologizing for being late... but she says he's right on time. She smiles, admitting she was afraid he wouldn't make it. "That was the old Fry," he says: "He's dead now." Later, as they share a romantic evening standing on a bridge, looking at the moon, Fry apologizes for losing the card he got her. She says it's okay. She doesn't really like cards. What she'll remember is their time together. Beneath the bridge, out of sight, Bender digs a grave for the other Fry, Bender, and Professor.