Early-Bird Cameo: Leela's parents appear in "I Second That Emotion" in the background as the two nosed mutant is telling the legend of a swamp monster, two seasons before "Leela's Homeworld" where they were formally introduced.
An eight-bit rendition of the Planet Express ship appears as the ship that Fry is piloting in an arcade machine called ''Monkey's Fracas, Jr." in the first few minutes of "Space Pilot 3000"/
The psychic hobo 9 that has an important role in the fourth movie can be seen in a crowd in the first episode of season 2.
Bender sounded more surly and drunken in his earlier episodes.
Also, in the pilot episode, it was mentioned that people in the year 3000 were implanted with career chips that permanently assigned them to a job, and if they quit, they would be fired out of a cannon into the sun. While the career chip plot device did creep up once in the series, the element of being fired into a cannon into the sun upon quitting a job was never brought up, as numerous times various members of the Planet Express Crew had walked off the job, disappeared without giving notice, and were fired, and in some cases horribly maimed or killed, only to wind up at the same job they were in at the end of the episode as though nothing had happened.
Zoidberg's running gag in the early episodes was that he was an alien doctor who didn't understand human anatomy. In the later episodes, the running gag is how much of a poor, desperate, disgusting loser he is. On top of that, he's shown as having teeth in his first few appearances.
In the earlier episodes, Professor Farnsworth was actually nice. A little dotty and lazy from old age, but nowhere near as heartless and insane as he would later be. On top of that, Billy West's voice for him was softer, and the episode that introduced Mom of Mom's Friendly Robot Company didn't even mention that Farnsworth and Mom used to be a couple (despite the scene of Mom confronting Fry right at Planet Express, there wasn't so much as a throwaway line about Mom and the Professor).
The earlier episodes were centered on the Planet Express crew going to strange new worlds. The later ones don't have these episodes as often.
Several episodes in Season 1 had cold openings, which were dropped near the end of that season (though "Brannigan Begins Again" from season two has the cold opening of Fry and Bender playing a violent, futuristic version of chess).
For those who are used to seeing the head of Richard Nixon as Earthican President, "When Aliens Attack" is going to feel weird to watch as it had an Earthican President named MacNeal (whom the Omicronians mistake for Jenny MacNeil from the legal dramedy Single Female Lawyer), though MacNeal's getting shot does set up for the events in "A Head in the Polls."
A subtle example appears in "In-A-Gadda-Da-Leela" when Zapp tricks Leela into thinking that Earth was destroyed and they're the last Earthicans left alive, and stranded on a suspiciously Earthlike planet.
Parodied in "The Late Phillip J Fry" where they find the Statue of Liberty blown up... then an Ape Statue of Liberty... than a Bird one... then a Lizard... then a slug maybe?
Inverted in the episode when Fry thought he'd gotten stuck in another cryogenic capsule for another thousand years, only to learn that the "post-apocalyptic wasteland" wasn't a (more) far-future Earth, but Los Angeles in Leela's time.
Ear Trumpet: When Fry travels in time and accidentally has sex with his grandmother when she was younger; upon having it spelled out for him she responds to his screams with "What was that dear?" and uses an ear horn.
There's one robot church that has an easy condemnation to Robot Hell for robots. According to his agreement with his new church, all Bender has to do is sin once to be dragged off to Robot Hell.
Robot Santa's naughty setting kind of falls under Easy Road to Hell. He condemns Scruffy to the naughty/death list just for picking his nose. Apparently Zoidberg is the only one who meets his standards.
Eat Dirt Cheap: After Lrrr accidentally conquers Earth the next thing we see is the main cast sentenced to the mines to supply his wife with gemstones to eat.
Eaten Alive: Justified examples in "Naturama" (it's nature red in tooth and claw and such after all).
Yivo's something between this and a Genius Loci. It ("Schle"?) is sentient and has enough area to store everyone in the entire universe but Yivo is also very personable and tries to interact with the universe without dragging everyone to itself ("schlimself"?) first. Yivo's also for all intents and purposes a living Fluffy Cloud Heaven, which gives Yivo another dimension.
Endless Daytime: The planet that cats originally came from doesn't turn, so they have perpetual night and day for different sides of the planet. They come to Earth to steal its rotational energy, resulting in the same situation for Earth.
Enemy Mine: Bender's Big Score has everyone forced to evacuate Earth to other planets by the scammer aliens, with the main characters taking up residence on Neptune. Unfortunately, they forget that Robot Santa is based there. It turns out that he's also been scammed, and Leela "convinces" him and his fellow holiday mascots to join forces and take out the scammers.
Enfant Terrible: Tonya in “Stench and Stenchibility” is revealed to be this.
In "Law and Oracle" the Minority Report-style prediction videos can be enhanced by doing a binocular-focusing hand-gesture.
Enormous Engagement Ring: In The Beast with a Billion Backs, Yivo proposes to the universe with one of these ultra-large rings.
Ensemble Cast: They've had a few, such as "Teenage Mutant Leela's Hurdles", "Three Hundred Big Boys", and "The Prisoner of Benda".
The Comedy Central-Era seasons in particular tended to focus on the entire crew in general.
Establishing Character Moment: Bender's alcoholism and tendencies to steal were established, in a few seconds (After seeming to "join in" on the emotional moment by putting his hand on top of Leela's, and, when he pulls it back, the ring is gone. Leela swiftly accuses him of stealing the ring, to which he admits he stole and then returns it, declaring "and now the mystery of the stolen ring has been solved! Let's have a drink!", pulling out three large beer bottles and then guzzling all three down at one time) in "Space Pilot 3000".
Even Evil Has Standards: The Robot Devil may be the embodiment of all that is evil, but Bender is worse, as seen in The Beast with a Billion Backs, where he reunites with his long-lost first-born son, then brings him to hell, and punts him through the Robot Devil's office into a vat of magma.
Robot Devil: Wow! That was pretty brutal, even by my standards. Bender: No backsies.
Exact Words: Invoked. The Constitution says that nobody can be elected president twice. Exactly, "No body", but Richard Nixon is just a head in a robot body.
Exotic Entree: Just to show how messed up the future is, some animals not considered food today are eaten regularly, like parrots. Not dolphins though, unless they blow all their money on instant lottery tickets, then it's okay.
The eyePhones are - you guessed it - inserted directly into the eyes.
A Martian Muck Leech attaches itself to Leela's eye in the fourth movie.
Leela's eye is apparently not as sensitive to the touch as regular human eyes; she can caress it.
Bender's eye is drilled into in the third movie.
The Faceless: Leela's boyfriend (or later ex-boyfriend) Sean is alluded to multiple times across the show's run, but is never actually seen (although he is described). He wouldn't be seen until the episode "Fry and Leela's Big Fling."
Fry: Listen, Leela. Thanks for rescuing me last night. Leela: Anytime. I actually enjoyed hanging out with you. Bender: Yep, everything worked out great thanks to good old Bender. Leela: Come on! It's not like you intentionally set us up with bad dates so we'd spend Valentine's Day together. Bender: Didn't I, Leela? Didn't I? (winks) (Iris Out) Leela:No, you didn't! You just rounded up a bunch of stiffs at the bus station and pocketed all our money.
Fake-Out Make-Out: Done between Fry and Leela in "A Flight to Remember" in order to convince Zapp Brannigan that Leela was taken
The ancient Professor and fat Hermes often get naked or dressed in skimpy clothes for little to no reason, aside from the future having left behind such primitive concepts as "modesty". Also, we really didn't need to see Brannigan as the Adam figure in the second 2010 episode. Augh. Also, Mom and the Professor on "Mother's Day."
Fry: "Nothing in here but a couple of elephant skin rugs. (beat) Eeew!"
Farnsworth: Oh yes.
Leela and Fry making out in the bodies of Zoidberg and Professor Farnsworth on "Prisoner of Benda." Good God!.
The second part of the Girly Calendar on "Neutopia". It starts out nice, then rapidly becomes very disturbing.
Shortly afterward, Leela declares that Bender has been down in the lava too long and she is going in after him. She starts to tear off her skimpy outfit (revealing some underboob) but is stopped by Professor Farnsworth who angrily reminds her that lava is hot. The DVD Commentary says they pushed it as far as they could.
"Why Must I Be A Crustacean In Love?" has Fry accidentally going into the women's steam room, where Leela and Amy are relaxing naked. Amy moves the hand covering her chest, but just enough to keep it still covered (according to the DVD commentary, the writers used this scene as a bargaining chip for the FOX censors when they wanted to get away with something that the censors would immediately decline, telling them "You let us get away with this. Why can't you do the same with this scene?").
Fry: Coed steam rooms? I love the future!
Leela: Fry, you're in the women's steam room.
Amy(aside to Leela): Psst! Look what life was like before genetic engineering.
Leela: Those poor 20th-century women.
(Fry swings his legs closed)
The straight-to-DVD movies kick it up a notch. The first one begins with a visit to the "Nude beach planet." In nonsexual fanservice, all the Continuity Nods qualify.
Additionally, a huge part of the first movie's plot revolves around Fry's ass, which is frequently bared.
The third movie has a scene where the whole crew takes a group shower together.
Excluding the Professor, although if he were there, it'd probably qualify as an immediate disservice to most fans.
Amy and Leela hug near the end of the third movie and then make out for a little while for no good reason.
In "Parasites Lost", the one in which Fry is infested with worms that make him smart, there are two fanservice scenes. One is of Fry, buffed up by the worms, ripping his shirt off. Another involves Leela sleeping in a VERY skimpy nightie as she waits for Fry to return.
The scene in "Rebirth" when Amy and Leela are ejected from the Stem Cell Tub may count.
The episode "In-A-Gadda-Da-Leela" has Leela wearing nothing but leaves to cover her naughty parts, eventually: at first she's covering her boobs with her hands, and not covering her front-parts with anything. Seriously, they might as well have inked in a little purple landing strip.
Leela as Clobberella in "Less Than Hero". Boy, is she sexy in that uniform and domino mask, and with her hair down. Lampshaded by her parents, who ask if she had to make the costume so revealing.
For added points, there's the scene where she tells her parents about being a superhero: she tears off her clothes showing the Clobberella uniform underneath!
In "Neutopia", most of the first calendar shoot. Particularly when Leela is wearing nothing on her upper body except suspenders. HOW DID THEY GET AWAY WITH THAT?
In "All the Presidents' Heads" we see Amy as if the British had won the Revolution. Needless to say, God Save◊ the Queen◊.
There is a nude conga line in "Time Keeps On Slipping":
Hermes: I don' know why I t'ought this would work.
In "A Taste of Freedom", the whole crew takes a nude bath in a hot tub to celebrate Freedom day.
In "Lrrreconcilable Ndndifferences", after Lrr's (staged) takeover of Earth, he and Ndnd are taking in a theatrical performance in which Calculon, the Professor and Leela are forced to fight a tentacled monster. Leela's outfit is pretty fanservice-y.
Leela and Amy showering together in "The Six Million Dollar Mon". Leela pleads with Fry to rub her new scented body oil on Amy and herself, but Fry is too busy trying to eavesdrop on a conversation between Hermes and Bender.
Stench and Stenchability has Amy in a nurses outfit. Complete with ass cleavage.
Well I'm not sure there's a rule against being a shellfish, and if anything it's even more of a reason not to eat them... Notably, he does eat a sea creature at his old scuttling ground. "Who's laughing NOW Vinnie?" (This was a different kind of crustacean, which is why it was small enough for Zoidberg to pick up, even though it bullied Zoidberg as a kid.)
Human meat is as kosher as pork and shellfish. (The latter is, however, directly banned by Book Leviticus.)
Another example of this trope is the above mentioned confusion surrounding the the specifics of robot religion. Fry sneaks into the reception for BOT Mitzvah (does this mean robots are circumsized?), while Bender falls under the spell of Preacherbot and the Church of Robotology, which rejects robosexuality.
Fry briefly consulted Father Changstein el-Gamal of the First Amalgamated Church, which features elements of Christianity, Judaism, Islam, Buddhism, Hinduism, and Atheism, or at least Agnosticism. And when someone asks whether the Space Pope is reptilian, he means "Yes".
"Oh why couldn't he have joined one of the mainstream religions? Like Oprahism?"
"Fantastic Voyage" Plot: Parasites Lost: The crew shrinks down to rid Fry of parasites, travelling through the ear, nose, heart, stomach, and intestines as they do so.
Fictional Colour: once made mention of a color called Blurple. Oh, and there was also Fry's description of an amazing, indescribable thing he saw that day at the beginning of I Dated A Robot:
Fry: I just saw something incredibly cool. A big floating ball that lit up with every color of the rainbow, plus some new ones that were so beautiful I fell to my knees and cried.
Amy: Was it out in front of Discount Shoe Outlet?
Amy: They have a college kid wear that to attract customers.
In a Black and White episode Fry's over-sized diamond ring creates a rainbow that combined with the shards of other diamonds created a brand new colour which was "in no way a combination of different colours". All we saw was a slightly different shade of grey.
Fictional Political Party: The one world government on Earth is run by a slew of these, most of which are puns based on the names of real parties and lobbyist groups in American politics. These include The Antisocialists, the National Raygun Association, and the Green Party (whose members are, literally, green), among others. Republican and Democratic parties are known as the Fingerlicans and the Tastycrats.
Fishing for Sole: In "The Deep South", after the crew receive a mandatory fishing license instead of a pet license for Nibbler, they head out to fish. Bender and Fry begin one-upping each other over past fish caught, while Leela busts out her harpoon to top them both. Unfortunately, the first thing she actually harpoons out of the ocean is a boot. Moments later she harpoons a crate of ten pairs of boots.
Amy: Oh, so this is where you shop for your boots!
Flipping Helpless: On the episode "Crimes of the Hot", Bender rescues a turtle because he feels a kinship with it, because he too can't get up when laid on his back. (He claims that all those times he got up from his back he was actually slightly on his side.) At the climax, when all the robots have to vent their emissions upward to save themselves, Bender and the turtle are on their backs, unable to get up. Then the turtle manages to flip over, which gives Bender the incentive to do the same.
Flowers for Algernon Syndrome: Fry's intestinal parasites improving his body and mind to near superhuman levels, then revert when he kicks them out.
Fluffy Tamer: Lrr and Nd-Nd towards Bigfoot in "Spanish Fry."
Flying Car: The default mode of transport in the 31st century. Even though there are plenty of wheels in evidence, the idea of attaching them to some seats to create a ground transport is apparently Lost Technology. In "Mother's Day" Fry literally reinvents the wheel to build a cart, and in "Game of Tones" Hermes describes a 1999 taxi as a "non-hovering hover-car."
In Bender's Big Score, Fry, now back to the 20th century, uses the code to go back in time a few more minutes to eat the pizza he was supposed to deliver. This minor event resulted in creating a time duplicate of Fry who eventually became Lars.
Foreign Wrestling Heel: When Bender joins the "Ultimate Robot Fighting League", he's shown as an All American Face squaring off against a montage of stock Heel characters. One such is named "The Foreigner." His antagonizing of the crowd?
"I'm not from here! I have my own customs!! Look at my crazy passport!!!"
Nibbler's shadow also appears for a brief second the moment Fry falls back into the cryo chamber.
Leela's parents can be seen in a crowd shot long before they're introduced.
Fry's brain slug starves to death. This may seem like a regular joke, until you find out that Fry lacks the delta brain wave.
French becoming a dead language was foreshadowed, or possibly a continuity nod, in the very first episode.
Blink and you'll miss it, but in "When Aliens Attack," when the camera zooms through the cosmos from Earth to Omicron Perseii 8, it passes by an Earth space probe engulfed in a blue, somewhat sparkly nebula. This is two and a half seasons before "Godfellas."
In "Rebirth", Bender, needing a new power supply post-rebirth, is implanted with a doomsday device to power him, but the device generates excess power which causes him to vibrate if he doesn't burn it off by partying. The first time he starts vibrating, you can see one of his eyes starting to get shaken loose. In the climax of the episode, Bender, refusing to party anymore, starts vibrating again, his eye falls out, and the cyclops-eating monster from earlier in the episode mistakes him for a cyclops and eats him... then the doomsday device goes off inside the monster, killing it and resolving Bender's excess energy problem.
"Freaky Friday" Flip: "A Prisoner of Benda" takes this trope and runs across the border with it, refusing to come back until extradited for its various crimes. They set up a rule that two bodies can only switch minds once, and then proceeded to work out whether they could eventually restore everyone's original bodies via group-theory. The episode contains a 3-second shot of nothing but Farnsworth's laser-blackboard showing the new, completely original theorem proved just for this episode. And they said abstract math doesn't have any real-world applications.
Free Wheel: Parodied — the wheel is coming from an exploding spaceship.
Friendly Sniper: As of "The Tip of the Zoidberg", Zoidberg, of all people, is revealed to be one, or at least capable enough to put three shots into a body with a fairly tight grouping.
Fun with Acronyms: Fathers Against Rude Television was a group made by Farnsworth and Hermes in response to Bender's decadence when he starred on All My Circuits in "Bender Should Not Be Allowed on Television".
Also, the Democratic Order of Planets, an intergalactic counterpart to the UN.
On "Saturday Morning Fun Pit," G.I. Zapp's enemies are part of a terrorist group called A.C.R.O.N.Y.M (A Criminal Regiment Of Nasty Young Men)
Fun with Flushing: Bender finally gets fed up with (or more accurately, jealous of) Nibbler and flushes him down the toilet. This prompts them to install a chip that forces him to feel Leela's emotions, causing him to flush himself (in pieces) so he can rescue it.
This comes after Bender realizes that he is too big to go down the drain as one piece:
Futuristic Superhighway: All cars are hovercars, so there are skylanes along with regular ground roads. In "Bendin' In The Wind" the Golden Gate Bridge is now a hoverbridge, so it doesn't need an actual road on it... which is a problem, since the gang is on a 20th Century VW Microbus. Intergalactic trucking routes and railroads are also present, and "Rebirth," the first episode after the series was Un-Cancelled, features the Panama Wormhole.
Gaia's Lament: Played for laughs. Pine trees, anchovies, cows, and poodles are extinct. Owls replace pigeons and rats as urban pests. Jungles exist on Mars but not Earth, and global warming was solved by dropping a piece of ice in the ocean every now and then. It was later solved by pushing the Earth away from the sun. In another episode, global warming was said to be solved with the nuclear winter.
Genius Breeding Act: In one episode, a Genius Breeding Act is referenced from a time when aliens landed on Earth and forced the smartest members to mate continuously. Farnsworth was disappointed that the latest alien invasion wasn't going to involve this.
Amy is an ABSOLUTE Ditz. However, as the episode "That Darn Katz" reminds us, she IS an engineering graduate student who designs a machine to harness the rotational energy of the Earth. Also, she officially gains her doctorate at the end of the episode, so she is the ultimate Genius Ditz.
Also Dr. Zoidberg. Even though he's the staff Doctor, he knows absolutely nothing about the Human Anatomy. We later find out that he IS a doctor - of Art History.
What's more impressive is that there were a couple of occasions where Zoidberg actually performed operations successfully. Impressive, considering he doesn't actually have any medical training. He may not know anything about human anatomy but he is a terrific alien Doctor.
Genre Shift: The first two seasons were pure comedy, with no emotional investment in the characters. Starting from the third season, they put some emotional investment into Fry and Leela's relationship, and had a couple twist endings that really made you feel something, the most famous examples being The Late Philip J. Fry, Jurassic Bark, and The Luck of the Fryrish. This was done the most in Season 4, which is why it's often considered the best season.
Get a Room!: Bender shouts this at an offscreen couple while he, Fry and Leela are climbing up the Watergate hotel. When one of them replies that they're in a room, he tells them to lose some weight.
Gilligan Cut: Used, along with most other cut gags, in "Time Keeps on Skippin'"
Leela: "Fry, stop. I don't wanna hurt you, but there is absolutely positively no way that you and I will ever, ever—" (time skip) Preacher: "—man and wife. You may kiss the bride."
It was used in the new season 6 episode as well, where the crew stumble upon a bus filled with skeletons of dead people. When Zoidberg shoves the bones off of a bed, the Professor scolds Zoidberg for desecrating the bones of the dead people. However, when Amy says that she found a safe, cut to Farnsworth using a skull to break into the safe
Girl on Girl Is Hot: Titanius Anglesmith (Bender) and Greyfarn's (Farnsworth) opinion on Leegola (Leela) and Gynecaladriel (Amy) making out in Bender's Game.
Titanius Anglesmith: Ah, can it wait a couple of minutes?
Greyfarn: Yes, yes it can.
Bender and Fry watching Amy wash the Planet Express Ship, aka Bender's current girlfriend (quite literally Cargo Ship).
God Guise: In "Godfellas", Bender ends up drifting in space, where he becomes God to the Shrimpkins, a race of miniature people who end up settling on his body.
After learning that Nibblonians have been around since the dawn of time, Leila asks them about the creation. After seconds of untranslated Niblonian gibberish, Leila exclaims "That means every religion is wrong!"
In "Overclockwise", Bender temporarily achieves omniscience, and obtains printouts with the answers to life's great questions. He casually throws away "the reason we exist", but does show Fry and Leela an account of their future together.
Godfellas is this trope in compact-episode form. Bender becomes a god, fails horribly, meets something that might be God, and then proceeds to learn the ultimate godly lesson:
Entity: If you've done it right, people won't be sure if you've done anything at all.
Going Critical: Better than most shows, but in "The Futurama Holiday Spectacular", Grandma's fruitcake reaches critical mass when thrown into Santa's sleigh, creating a small mushroom cloud.
Leela: Hmm... If we can re-route engine power through the primary weapons and configure them to Melllvar's frequency, that should overload his electro-quantum structure. Bender: Like putting too much air in a balloon! ... Leela: It's not working! He's gaining strength from our weapons! Fry: Like a balloon and... something bad happens!
Good News, Bad News: Whenever the professor says "Good news, everyone!", he's inevitably going to announce something horrible. Parodied in one episode when he's announcing something even worse than normal and simply says "News, everyone!" in exactly the same tone of voice as normal and lampshaded in "The Sting" when he says (in exactly the same tone of voice as normal) "Bad news everyone! Now normally when I say "Good news" it's usually bad news. So you can imagine how bad this news actually is." Also, in another episode, the Professor purchases some IKEA πKEA science instruments which... go exactly how you'd expect them to. He is blown through the wall in to the next room. As he stands up, he says "Bad news, no one."
In the "Freaky Friday" Flip, he and Amy try to switch to their original bodies. When they fail, he says "Bad news, me."
Good Night, Sweet Prince: Mentioned twice on the "Anthology of Interest" episodes (both at the end of an act one story where Bender ends up dead — in Anthology of Interest 1, Bender gets impaled on a skyscraper. In Anthology of Interest 2, Bender [who has been turned human] kills himself with excess eating, drinking, and partying).
Grand Finale: The series has had four different episodes intended to act as this in case it didn't get renewed: the last episode of the original run, the last movie, the last episode of Production Season 6 (which was produced before they were renewed for a 7th production seasonnote the show's renewal was confirmed several months before the episode aired) and the last episode of Production Season 7.
The first one was "The Devil's Hands are Idle Playthings", which was notable for featuring music more prominently than any other episode in the series. It ended with badly made holophoner images of Fry and Leela walking off into the sunset holding hands.
The second one was Into the Wild Green Yonder. They really tried with the ending, which had a cliffhanger of the crew about to hit a wormhole, but they just got blasted back to Earth when the series restarted on Comedy Central.
The third was "Overclockwise". It ended with Fry and Leela looking at a paper with the future of their relationship and smiling.
The fourth will be the finale of the seventh production season "Meanwhile", which may very well prove to be the final finale.
Grand Romantic Gesture: Fry pulls off one so big Leela decides to marry him. Unfortunately, time skips over the gesture itself and neither of them can remember what it is. It turns out to be a love note... written with stars Fry rearranged in space.
Green Aesop: Parodied in "The Bird-Bot of Ice-Catraz" and "Leela and the Genestalk". In the former, Free Waterfall Sr. is dead-set on saving the lives of Antarctica's threatened penguin population until he learns the birds are breeding out of control, at which point he organizes a cull to kill them in the most agonizing ways imaginable. In the latter, while it's shown that Mom's agribusiness holdings are run purely for her own greed than any sort of charitable motivation, they have managed to cure various diseases and breed fast-growing crops (which, by the end, have totally blanketed New New York).
Grey and Grey Morality: "Benderama", interestingly enough. The giant starts smashing up everything, only because he has some self-esteem and anger issues and everyone is insulting him. Everyone except Bender is entirely drunk and so can't really be held accountable, and while Bender stops the giant, he really was the only sober one and isn't any better than everyone else drunk:
Bender: Let this be a lesson about attacking those more handsome than oneself.
Grey Goo: Done with the infinitely replicating Benders, which even drop the trope name. They only thing saving the world was the Benders' collective laziness. The do leave behind significant damage before leaving to avoid doing even a minisulce fraction of a thing.
Groin Attack: Subverted in "Why Must I Be a Crustacean in Love?" when an unwilling Fry must duel Zoidberg for the claw of the lovely Edna:
Zoidberg: I want the tactile pleasure of chopping him right here, in the gonads! *points approximately to Fry's collarbone*
Fry:Nobody correct him!
Hair Trigger Explosive: Fry is carrying sticks of dynamite, and each time one fell off it exploded. Fry makes it to the storage shed, there's a big explosion inside, and Fry emerges singed. Of course, the whole point of dynamite is that it doesn't explode unless detonated, so this was strictly Rule of Funny.
Hand Wave: "I thought that machine made noses?" "It can do other things. Why shouldn't it?" (Granted, that all makes perfect sense.)
"Hey, You!" Haymaker something like this happened in "I Second that Emotion" one of Bender's arms tapped a foe on the shoulder, pointed in another direction, then the other arm punched said foe in the face.
High-Class Glass: Bender puts on a monocle to show how rich Fry becomes in the episode "A Fish Full of Dollars".
Leela: I know Fry's rich, but do we really have to wear these top hats?
Bender: Maybe you don't understand just how rich he is. In fact, I think I'd better put on a monocle.
High Fantasy: The theme of the world Bender invents (and then everyone gets transported to) in Bender's Game.
Hippie Van: In "Bendin' in the Wind", an ancient, abandoned VW bus is discovered. After Fry explains how it works, the crew get it repaired and go off on a hippie - themed road trip, following the band "Beck" on their "Bendaid" tour.
In Decision 3012, Nixon displays a sign saying, "Kick him around for four more years," a reference to Nixon's real 1962 Goodbye Speech.
History's Crime Wave: A Holodeck malfunction causes Amy and Kif to get attacked by Jack the Ripper, Attila the Hun, the fictional Professor Moriarty, and Evil Lincoln.
Hitler's Time Travel Exemption Act: Double subverted in "The Late Philip J. Fry." Professor Farnsworth succeeds in assassinating Hitler when his time machine has to cycle through the death and rebirth of the universe, but they miss their intended time period and are forced to travel through time a second time. His haste this time around causes him to miss and assassinate Eleanor Roosevelt instead.
Hoist by Their Own Petard: The worms in "Parasites Lost". They make Fry smarter and stronger, and he uses his newfound smarts and strength to get them to leave.
Holiday Volunteering: In the episode "Xmas Story" Bender volunteers at a Liquor Kitchen (for homeless robots) only to pose as a homeless robot himself and drinks all the free booze. In the end he invites some of the robots back to have Christmas dinner with the rest of planet express.
Hollywood Density: Parodied as starship fuel (dark matter) is so dense that "a single pound of it weighs ten thousand pounds." In one case, Fry refers to a ball of this fuel, which has previously been shown on rare occasions to be liftable by a human, as "weighing as much as a thousand suns."
"The Game" throws the dark matter's weight out the window by having the characters pushing wheelbarrows filled with it. On the sun.
A lampshade gets hung on this when Fry and Leela are going to have a fiddle contest with the Robot Devil where the prizes are Bender's soul and a solid gold fiddle. When Fry (of all people) asks "Wouldn't a solid gold fiddle weigh hundreds of pounds and sound crummy?" the Robot Devil admits that it's mostly for show, then (being a robot) takes it and plays a complicated piece on it.
Then Bender grabs some wings and begins to fly out of Robot Hell carrying Fry and Leela. When Leela tells him he needs to fly faster he says he could if she would drop the solid gold fiddle she was carrying (dented from hitting the Robot Devil over the head with it).
Leela is once impressed with a handsome doctor, which makes her all flirty: "A tall doctor, you say?" His name is Adlai Atkins and they grew up in the same orphanage. He's an eye surgeon, and it doesn't hurt that most doctors are rich.
The movie had a sexy young doctor named Dr. Cahill, (although Fry just called her Dr. Good and Sexy) who — despite her insistence that her attractive nature didn't make her a bimbo - was in fact a Brainless Beauty of a bimbo.
Scientist: I have combined the DNA of the world's most evil animals to make the most evil creature of them all! (A naked man walks out of the chamber) Naked Man: Turns out it's man.
Humans Are Morons: The 20th Century is known as "The Stupid Age" to historians. However, that doesn't make humans of the 31st Century any less stupid than us.
Humans Need Aliens: Although Nibbler acts as a cute little pet most of the time, he in fact belongs to a powerful alien race and saves Earth and humanity more than once.
Hurl It into the Sun: Hermes and the box in "The Farnsworth Parabox". Also done with a shipment of popcorn kernels in "A Bicyclops Built for Two" and a shipment of candy hearts in "Love and Rocket", although in that episode it was a quasar instead of the sun.
Hurricane of Puns: Numerous examples, but the one that really takes the cake is the Lead In to "The Luck of the Fryrish", containing every joke imaginable about horse racing, and, Just for Pun, a joke about Quantum Physics.
In Bender's Game, following a particularly brutal Take That to Robin Williams (in form of a horde of Morks, a combination of orcs and, well, Mork who can only repeat his catchphrases and are messily slain in great numbers for being annoying) for supposedly not being funny, we are subjected to The Eviscerator, which seems like the exact kinda joke Williams would make in his stand-up routine.
"That Darn Katz" has Nibbler claiming that nothing acts cute without an ulterior motive. Even keeping in mind his actions through the entire series, he follows this up by acting cute to trick Amy into changing his diaper.