In "Crimes of the Hot", a call is put out for a global meeting of scientists. The one man who runs up claims to have a degree in homeopathy (from Evergreen College, which was Matt Groening's alma mater). The announcer informs him he has a "Degree in Baloney" and shoots him in the face with a water cannon.
In "I Second that Emotion", Fry, Leela and Bender visit the Sewer Mutants underneath New New York, whose entire civilisation is built out of things people have flushed down their toilets. Eventually they get to their library:
In "Yo Leela Leela", Leela warns everyone not to get to excited about the premiere of her kids' show, because "...we all know any show that's remotely good gets canceled. Sometimes two or three times."
Also, Amy's line about Rumbledy Hump having a Periphery Demographic of adult hipsters who ironically love the show because of the low-budget sets and costumes.
One of the new shows on Ticklelodeon is Popular Slut Club, which is a slightly exaggerated burn on all the Disney and Nickelodeon kidcoms that are filled to the brim with candy-coated sexual innuendo.
In "Lrrreconcilable Ndndifferences", the gang visits Comic Con. The entire sequence is strewn with subtle Take Thats, but the part where the pilot of a new show— Futurella— is shown off by its creators takes the cake, as the show is canceled five seconds into the intro.
Matt Groening: Wow. Fox has really streamlined the process.
In "A Clockwork Origin", the entrance sign for Odulvai Gorge reads "Birthplace of Ryan Seacrest... And The Rest of Mankind"
The episode "Overclockwise" takes a stab at technology manufacturers for their somewhat draconian policies on dealing with people who mod their consoles.
In "Bender's Big Score" a Family Guy calendar can be seen in the background. It advertises that it includes a season's worth of jokes from the show, which comes out to one per month.
"Mars University" takes a jab at professors:
Farnsworth: Please, Fry! I don't know how to teach. I'm a professor!
The scammer aliens in Bender's Big Score. Infantile Trolls that derive great pleasure in kicking the dog, the writers did everything in their power to portray them as sick, deviant, and with no sympathetic or positive traits whatsoever.
From "Mobius Dick":
Amy: You've gone from crazy like a fox to crazy like Fox News!
Speaking of Fox News, one of the reporters in "Decision 3012" says this:
Scoop: Scoop Chang, Fox Quote-Unquote News.
Actually, the entire episode is a pretty big take that to the conservative side of the birther issue, Nixon, and Republicans in general.
From "Law and Oracle"
Pickles: Do you have any idea what a burden it is to know everything that will ever happen?! To never be surprised. To know the punch line of every joke hours in advance?!
(in "I, Roommate," Fry and Bender search for a new apartment) Fry: Well, I give up. What's the catch? Apartment salesman: Oh, no catch. Although we are technically in New Jersey. *Smash Cut to Planet Express* Fry: Not one place even remotely livable. (in "A Big Piece of Garbage," the crew watches a documentary about New York running out of places to empty its garbage) Narrator: The landfills were full. New Jersey was full. (in "Hell Is Other Robots," Fry and Leela discover Robot Hell) Leela: Who would've thought Hell would really exist, and that it would be in New Jersey? Fry: Actually... (in "Attack of the Killer App," Leela notices a disgusting odor on Fry) Leela: What stinks? Were you rolling around in New Jersey? (in "All the Presidents' Heads," the Continental Congress meets in 1775) Thomas Jefferson: The yeas have it. Our nation's official joke state shall be New Jersey. (in "Stench and Stenchibility," Zoidberg and Marianne—who has no sense of smell—go on dates at a limburger restaurant, a petting zoo of pigs and skunks, and New Jersey)
Also from "All the Presidents' Heads":
Farnsworth: I'm sure no one's ever said this before, but I must get to Philadelphia as quickly as possible!
Tangled Family Tree: The Fry-Farnsworth-Mom family tree is surprisingly complex when you sit down and draw it.
The Teaser: The earlier episodes had cold openings before the credits. "Space Pilot 3000" (the very first episode where Fry wakes up in the year 2999 after slipping in the cryogenic chamber) is the only one where the teaser has a connection with the actual episode.
Techno Babble: subverted multiple times by many of the main cast. Scenes requiring a pseudo-scientific explanation often invoke the use of gibberish in the place of more traditional, partially plausible Applied Phlebotinum.
Bubblegum Tate: Looks like what we got here is a chronoton mass in the sub-atomic inferencees.
Prof. Farnsworth: Yes, something involving that many BIG words could easily destabilise time itself!
More like "paradox correcting". Pretty much every paradox that shows up (The second Nudar, Hermes' body, Lars) gets destroyed ("corrected") by the universe eventually. The one exception may be the thousands of Benders at the end. Not even the Universe could handle that much paradox.
Bender: ...What? Hermes: This place is crawling with yous! Bender: So there's more Benders around. As far as I'm concerned, that's good news! Farnsworth: Bad news, everyone!
Tentacle Rope: To name just one, the short scene in "A Farewell to Arms", complete with suction marks all over Leela. (The monster pays dearly for his transgressions...) Probably a dozen more FanService instances could be listed - and the scene with Yivo already smells like redlink....
That Man Is Dead: Made humorously literal in "The Late Phillip J. Fry". When Fry shows up on time for Leela's birthday dinner, she admits she didn't think he'd actually do so. Fry tells her that the Phillip J. Fry that stood her up before is dead... because through the use of the Professor's forward-only time machine, the Professor, Fry, and Bender have cycled all the way through their universe and an additional one to get back to their relative present, killing the Professor, Fry, and Bender of the latest iteration of the universe upon arrival.
Three-Laws Compliant: In "Free Will Hunting", Prof. Farnsworth reveals that he designed Bender's operating system, which prevents him from picking up a free will unit or attempting to kill his programmer.
Professor Farnsworth: Anyhoo, your net-suits will allow you to experience Fry's worm infested bowels as if you were actually wriggling through them.
Dr. Zoidberg (cheerfully): There's no part of that sentence I didn't like!
Throw the Dog a Bone: Jurassic Bark, perhaps the most notorious Tear Jerker in the series so sad that it even brought the crew to tears. The first direct-to-video movie, Bender's Big Score, softened the blow by creating a timeloop where Fry returned to the past and got to live a life with Seymour, so instead of waiting 12 years for Fry to return before getting petrified, Seymour actually got live a happy life.
Time Abyss: The Nibblonians were 17 years old at the time of the Big Bang, and the Brainspawn came into existence 1 millisecond after.
Time Is Dangerous: The final episode deals with the Professor inventing a Reset Button that reverts ten seconds. He has a time-proof chamber that those outside of the time bubble can sit in to avoid the affects of the jump. A collision of interactions between chronotons and anti-chronotons causes objects from the chamber to disintegrate upon leaving however.
Time Passes Montage: In "Space Pilot 3000", we have this type of montage while Fry is frozen. It wouldn't be the last time this trope is utilized.
Used to soul crushing effect in "Jurassic Bark", where Seymour is seen waiting for him on the curb outside his old workplace for 15 or so years, until he lies down and dies.
Both of these were among the things nodded to in Bender's Big Score. Both times, a time-traveling Bender was responsible. It also shows that the dog was being watched after by an alternate Fry, somewhat lessening the impact of the preceding episode in hindsight.
It's also used breathtakingly in the climax of The Late Philip J. Fry when Fry, Bender and the professor witness the end and beginning of the universe.
Time Travel: At one point, the Professor builds a time machine that can only go forward. He has Bender and Fry help him test it, but they end up in the year 10,000.
In "All the President's Heads", Farnsworth discovers that licking the heads in the Head Museum causes one to travel briefly to the time period that head lived in.
Bender: This is a simple matter of justice! And normally, I'm against that.
Farnsworth isn't actively evil, but he has a near-total disregard for human life, has built a ton of Doomsday devices for reasons which are unclear, and once okayed the destruction of an entire planet because "There is no scientific consensus that life is important!" (though he did turn around in the end).
Tom Hanks Syndrome: In-universe example with Harold Zoid, once a famous silent comedian, turned drama director.
Tomato in the Mirror: Happens twice in "Rebirth": first, when Robot Leela finds out that she's a robot, second when it's revealed that the Fry we've been seeing for the entire episode was a robot too.
He also seemed to have gained a lot of self-confidence by the end of the episode.
Zoidberg's been earning a lot of Badass Points since the move to Comedy Central.
Fry gets a temporary one when he becomes a surprisingly competent cop.
Top Ten List: Zapp Brannigan reveals Bender's ten most frequently used words in this manner during "War is the 'H' Word". For the record, the words are:
#6: Pimpmobilenote Censored to "of course" when shown in the UK
#2: Daffodil (as in "Hot diggety daffodil!")
Touch of the Monster: "Calamari Surprise" version on the cover of "The Beast with a Billion Backs", showing Leela in a skimpy nightdress struggling in the grip of Naughty Tentacles as the rest of the cast look on in horror.
Troperiffic: this show is pretty much the embodiment of this trope. It celebrates in every single cliche and trope, and often uses Rule of Cool just because it is so freaking awesome.
Trouble from the Past: The future of Futurama may not be a utopia, but poverty has been mostly eliminated; however, it came at the expense of many a Dystopian Edict. The unemployed are forced to take jobs against their will, the remaining poor have been sent to insane asylums, and mutants are forced to live in the sewers. Also, in the episode "A Big Piece of Garbage", the people of the 31st century have to deal with the garbage problems of the 21st century.
Trouser Space: While thinking he is a robot, Fry takes some sandwiches from his pants and offers them to his friends. They are not interested.
True Companions: The Planet Express crew, no matter what they go through, will always pull together for each other in the end.
Sure, Robot Santa Claus is evil now, but as originally designed he shouldn't be that scary.
One episode has a robot nanny who not only looks frightening, but speaks in a loud, angry voice and claims to have replaced the baby's mother before feeding it with a bottle from its toothy maw. Leela thinks it's cute. Notably, the baby doesn't seem to mind either.
Un Paused: In the pilot, Fry pushes Leela into a stasis pod mid-lecture, and sets the release time for later that day. When she comes out she's still yelling at him.
Uranus Is Showing: According to Professor, astronomers changed the name of the planet Uranus to stop that stupid joke once and for all. It's now named "Urectum".
Useless Accessory: Bender and many other robots have antenna that serve no apparent purpose, which gets a Lampshade Hanging several times. First when the thing turned out to be interfering with the satellite transmission in his new apartment, and Fry says he should just cut it off since it doesn't do anything, after which it's treated as a robot equivalent of his penis. Again when it's suggested he has a toilet somewhere in his body and pushing down on it flushes.
Subverted again when Mom says most people think she puts antenna on her robots just to make them "more science-fictiony" but they really let her take control of everything with a remote control.
The antennae also allow DOOP to take military control of the robots.
"My Three Suns": A machine selling "Refreshing Crack" gets stuck, and the customer whines "Don't hold out on me, Man!"
"Mother's Day": All the machines rebel against humanity, including a coffee machine that sprays its contents at Fry and a vending machine that shoots cans at people.
"I got a big, big thirst for human blood!"
"The Bots and The Bees": Bev, the new beverage vending machine at the office, hates Bender and insults him at every occasion. Soon the two start fighting, which then leads to lovemaking, which leads to Bev having a baby.
In the episode "Ghost in the Machines", one of Bender's methods in his attempt to kill Fry involved possessing a vending machine that serves pineapples and has them launch at Fry when he tries to make a purchase.
Vetinari Job Security: Hermes apparently has this at Planet Express. During the events of "Lethal Inspection," he leaves Leela in charge for a few days. During that time things fall apart completely: he returns to find that the ship has been repossessed, unexplained alarms are going off, the Professor is trapped in a giant beaker, Leela has been reduced to a gibbering mess, and the crew is preparing to cook and eat Zoidberg. It only takes him an hour to get things back to normal.
Viewers Are Geniuses: There are a lot of complex jokes on science, science-fiction, and engineering and mathematical principles.
Violent Glaswegian: Parodied in "Yo Leela Leela" with Extreme Toddler Wrestling held in Glasgow, Scotland.
Virgin Sacrifice: In 'I Second That Emotion', Leela is a virgin sacrifice to lure out sewer monster El Chupanibre, despite the fact that the sewer mutants have seen Zapp Brannigan's website.
Virtual Reality Interrogation: In one episode, MOM wanted to get Fry's bank information. Since his PIN was related to his old job in the twentieth century, her sons set up an elaborate hoax to convince him that coming to the future was All Just a Dream and he was back in his old life.
Zapp and Kif seem to be a more extreme and subtle example, though it's usually always Kif showing the hidden friendship aspect, not Zapp.
Vocal Evolution: Many examples, but the ones that stand out the most are Hermes, Morbo, Bender, and Professor Farnsworth. Hermes had a much deeper voice, his accent slightly more prominent. Likewise, Morbo had a more prominent guttural tone to his voice, but now, it only shows when he coughs.
Voodoo Shark: Parodied. Often. Hell, the most prominent example is the page quote.
Wallpaper Camouflage: In "Lethal Inspection", Hermes is wearing a shirt the exact same color as the wall behind him, just as Leela talks about how bureaucrats blend into the walls.
Wealthy Yacht Owner: Duchess de la Roche, the wealthy robot Bender dates in the episode "A Flight to Remember". She doesn't just own a yacht, she is a yacht.
Weaponized Landmark: Done as a variation with 20th Century Fox's iconic searchlight logo, which is an actual building in Hollywood. The tour guide explains that the searchlights are designed to blind pilots so Fox can film the resulting crashes for their reality shows.
We Have Reserves: The way that Zapp Branigan defeated the rampaging killbots from the Octillian System. You see, Killbots have a preset kill limit. Knowing their weakness, Zapp sent wave after wave of his own men at them, until they reached their limit and shutdown. Kif, show the tropers the medal he won.
We Will All Fly in the Future: In the world of Futurama, they do not even know what a wheel is because all cars have been floating, flying, and/or hovering for so long that wheels are too ancient to remember. And if that doesn't fit the bill, they also have tubes that wind through the city of New New York that people hop into and are whisked away in to whatever destination they need to get to in the city. And if that is still not enough to qualify, they also have every other means of insta-flight available to them. Such as rocket boots, antigrav belts, and jet packs. Want to fly in Futurama-verse? Pick your poison.
"Well Done, Son" Guy: Apparently Lrrr's reason for entering the Universal Poker Championship during the events of "Into the Wild Green Yonder" was to win his father's approval.
We Will Have Perfect Health in the Future: Subverted on a few counts. The Professor's back, memory, and mental stability are often called into question; Leela is put in danger by giant space bees, Zapp Brannigan claims to suffer from the "very sexy learning disability" of Sexlexia (though that's most likely a cheesy pick-up line, as this is Zapp Brannigan we're talking about)—even the robots get sick!
On the other hand, the average human lifespan has been extended to the point where robots collect people when they turn 160, then process them as energy in pods à la The Matrix.
Certain conditions that used to be fatal, such as decapitation, can be recovered from pretty easily. On a related note, it seems blood has also been totally replaced by medication and nanobots.
Even Americans that have been taken over by Britons in an Alternate Universe are not immune to this, as proved by "All The President's Heads". Given a brilliant lampshade by a Cockney version of Bender.
"Oy, 'ow come we Brits got unionized healthcare, but our teeth still look like this?"
What Is One Man's Life in Comparison?: In The Why Of Fry, it's revealed that Fry was frozen by Nibbler so he could live long enough to fight the Brain Spawn. While explaining himself and trying to convince Fry to go through it all over again, Nibbler asks the all important question of "what is one man's life weighed against the entire universe?"
Parodied in "Why Must I Be a Crustacean in Love?", when Fry tries to help Zoidberg to get a woman.
Zoidberg: I'm confused, Fry. I'm feeling a strange new emotion. Is it love when you care about a female for reasons beyond mating?
Fry: Nope. Must be some weird alien emotion.
Wham Episode: The last few minutes of Luck of the Fryrish. It doesn't get any less shocking or impacting on further re-watches, either.
The last few minutes of Jurassic Bark as well.
Most likely because these two episodes are so shocking and emotional, they're considered to be some of the best and most memorable Futurama episodes out there and are frequently included on people's "best of" lists.
Wham Line: The end of "Into the Wild Green Yonder" pulls a double whammy:
Leela: (to Fry) Maybe I waited too long to say this, but I love you too. (Interrupted) WORMHOLE!
What Measure Is a Non-Human?: Often Played With. Zig-Zagged as per the Rule of Funny when it comes to the robot society: In one episode, robots have the vote, and are the most important demographic in an election; but in another episode, damaged robots are unceremoniously destroyed and turned into recycled cans. Some robots seem to be independently wealthy, and even employ human servants; but sometimes, robots are explicitly said to be mere tools meant to make human lives easier.
Why Do You Keep Changing Jobs?: Sal, the morbidly obese redneck, is always seen in a different low-level job, primarily one that involves heavy lifting. It's even mentioned in the audio commentary for the second episode that the writers frequently debate on whether there are many clones of Sal, or if he just keeps moving from job to job.
Likewise, "Fishy Joe" Gillman will always open a new fast-food restaurant after the previous one fails.
And Abner Doubledeal, who went from managing Ultimate Robot Righting to managing The New New York Mets to being Executive Producer of the Ticklelodeon Kids Network.
Will They or Won't They?: Fry loves Leela despite her being a mutant. Leela rarely reciprocated, until the end of the fourth movie, and it's stuck. The new season has them together, but it's done subtle enough in most of the new episodes that you wouldn't know it if you didn't look for it (For example, Leela instantly agreeing to join the "mile deep club" in "The Duh-Vinci Code"), but some make it obvious (All of "The Late Philip J. Fry").
And the next season after that has them going on regular dates, Leela initiating her share of the romance (asking Fry if he wants to join the "Balcony Club", for instance), and her referring to Fry as her boyfriend.
Wiper Start: In "Space Pilot 3000", Fry attempts to start up the Planet Express ship by himself, only to activate an automatic coffee machine, leaving him with a dumbfounded stare.
Worthless Foreign Degree: No degree and being out of time instead of out of space but the basic principle is the same. In one episode, Fry was told that being a college drop-out back in his pre-freezing days was like being a High School drop-out in the series' time. Wating the same respect he believes college drop-outs have, he enrolled at Mars University just to drop out. He even took it as a compliment when Leela told him he'd not last two weeks.
Bender: Blackmail is such an ugly word. I prefer 'extortion'. The 'X' makes it sound cool.
In a more meta example, Producer David X. Cohen said he changed his middle initial from the original "S" (which he used when he worked on The Simpsons) for two reasons: 1) there was another writer that went by the name "David S. Cohen" and Writers' Guild of America union rules state that no two film or TV writers can have the same name, and 2) "X" makes his name sound "science fictiony."
Yandere: Interestingly enough, the Planet Express crew's primary mode of transportation, as seen in "Love and Rocket".
You Go Girl: Played with in the Blernsball episode. Leela is awed at the chance to be the first woman to play the sport in the Major League, despite being told up front that it's a stunt hire because she's so entertainingly awful. Then she's discouraged when she realises she's actually making it harder for female athletes to be taken seriously, and resolves to become at least slightly competent. She fails, but her opponent consoles her with the fact that she'd made lots of other female players determined to prove they don't all suck as much as she does.
You Wouldn't Hit A Guy With Glasses: In "How Hermes Requisitioned His Groove Back", Bender is caught cheating in a game of poker using X-ray glasses. When he's cornered, he nervously states, "Hey...you wouldn't hit a guy wearing X-ray glasses, would ya?" Unsurprisingly, it doesn't work.
Your Mind Makes It Real: In "Forty Percent Leadbelly", Bender becomes a folksinger and finds that everything he sings about comes true. This is because his mind is accidentally left connected via wireless to a 3-D printer he used to recreate a famous folksinger's guitar, which keeps creating things from Bender's memory.