Futurama Time Keeps on Slippin
"Time Keeps On Slippin'": Season 3, Episode 14

In order to grow a mutant basketball team to compete against the Harlem Globetrotters (they "came to terrify and humiliate" us, not entertain us with their sports comedy antics), Professor Farnsworth sends his crew out to gather chronitons particles, causing his creations to mature faster but also making time start skipping forward, leading to the possible early end of the universe. Fortunately, the Globetrotters also possess brilliant scientific minds, and are able to help figure out a way to use one of the professor's doomsday devices to stop the time skippage -- though nothing can aid Fry in his quest to figure out how he can win Leela over romantically.

Futurama The Why of Fry
"The Why of Fry": Season 4, Episode 10

The Brainspawn are back in this episode, this time working to collect all knowledge in the universe and store it in the Infosphere, their massive memory bank, after which they'll destroy everything else (why keep the hard copy when you have a digital backup?). And once again, our hapless delivery boy Fry is the only one who isn't affected by the Brains' powers, for reasons we finally learn. Fry turns out to be the "most important person in the universe," though he and the Nibblonians are the only ones who know it -- and for all that heroism, Fry does for once get a kiss from the one-eyed object of his affections.

Futurama Beast With a Billion Backs
"The Beast with a Billion Backs": Season 5, Episodes 5-8

It's love that could potentially destroy the galaxy in this straight-to-DVD feature that was broken up into four season-five episodes. A lonely Fry sneaks through a rift in the universe and meets giant tentacle monster Yivo on the other side, who takes over his mind by attaching an appendage to his neck. Soon everyone is worshiping the tentacle at its own behest, until Leela discovers that the alien is actually mating with everyone on Earth simultaneously. It promises to "start over as friends and see where things go" and starts wooing our universe with dates and promises of commitment to persuade everyone to head to Yivo's dimension forever -- hey, there doesn't always have to be mass destruction for the world to end.

Futurama That Darn Katz

"That Darn Katz!": Season 6, Episode 8

Finally, "Futurama" comes up with aliens even more adorable than Nibbler -- in this Amy-centric episode, a race of evil but irresistible intelligent talking space cats who've been living among us since Ancient Egypt plots to harness the Earth's rotational energy and send it, via the Great Pyramid of Giza, to their home planet of Thuban 9. They use the technology from Amy's doctoral thesis and their powers of hyper-cuteness to build an invention that stops the Earth from spinning, leaving one side freezing and the other too hot until she comes up with a way to fix things (or at least restore them to a reasonable approximation of how they were before). Chalk up a win for dog people everywhere.

Futurama Benderama
"Benderama": Season 6, Episode 17

Eric Drexler's nanotechnology, end-of-days, "grey goo" scenario gets reimagined in this episode, in which Bender creates increasingly smaller copies of himself while consuming more and more of the planet's matter. Before everything gets too close to being consumed by a grey Bender goo, the duplicates run out of alcohol and expire -- only a few survive and work their way down to molecular scale. It's not quite the destruction of all matter, but they do turn all of the Earth's fresh water into alcohol, making the world's population too drunk to deal with the giant angry alien (voiced by Patton Oswalt) that arrives looking to offer an apology -- which is dangerous in its own, goofier way.