Thanks to Professor Farnsworth's invention of the Smelloscope, which allows people to sniff for distant cosmic objects, the Planet Express crew discovers a giant ball of garbage hurtling toward New New York City. It turns out to be 20th-century trash returning home after having been shot out into space a thousand years ago, and to save everyone from being annihilated by a gob of America Online floppy disks and coffee grounds, Fry has to teach the refuse-free future how to litter in order to create an equal-sized garbage ball that they can shoot back at the incoming one. Problem solved! Or at least delayed for another millenium or so.
The warlike residents of Omicron Persei 8, a thousand light years from Earth, invade because a long-ago broadcast of the "Ally McBeal"-like "Single Female Lawyer" (about, as Omicronian Emperor Lrrr explains, "an unmarried human female struggling to succeed in a human male's world") was interrupted by what turns out to have been an act of klutziness by 20th-century Fry. It may be one of the worst reasons ever to attack and threaten to destroy a planet, but who can fault a dedicated fan? Since videotapes were destroyed in 2443's second coming of Jesus, the Planet Express crew ends up re-enacting a version of the show based on Fry's vague memories of it, proving that watching a lot of TV can actually help you save the world.
"Mother's Day": Season 2, Episode 14
When Mom, the beloved corporate overlord of Mom's Friendly Robot Company, decides to become "supreme overlord of Earth" because she's feeling bitter about an ages-ago affair that went sour, she decides to doom the human race to extinction for Mother's Day so that "everyone will hate it as much as I do." She uses her powers as manufacturer of the world's robots to start a robot rebellion that sends people screaming through the streets as giant androids tear down buildings, TVs attack and Bender... acts normally. It's then up to Professor Farnsworth to rescue everyone with a feat of elder love.
"The Day the Earth Stood Stupid": Season 3, Episode 7
Giant floating brains turn out to be Earth's greatest nemeses in the universe of "Futurama" -- we first see them in this episode, in which the Brainspawn attack the planet and render everyone an idiot with their stupidity rays. Only Fry is immune, but he's never been the brightest bulb in the basket in the first place. He does, however, have enough knowledge to divine where the leader of the invading force resides by thinking about where brains would obviously hang out -- at the library. Fry traps the Big Brain in a story of his own creation ("a crummy world of plot holes and spelling errors") and makes him leave the planet "forever, for no raisin" -- one of the show's great line deliveries from Maurice LaMarche.