Per "A Clone of My Own"
Farnsworth: These are the dark matter engines I invented. They allow my starship to travel between galaxies in mere hours.
Cubert: That's impossible. You can't go faster than the speed of light.
Farnsworth: Of course not. That's why scientists increased the speed of light in 2208.
This neatly explains why the ship is ...
For the money
Fry: This is awesome! Are we gonna fly through space fighting monsters and teaching alien women to lurve?
Farnsworth: If by that you mean "transporting cargo" then yes. It's a little home business I started to fund my research.
Space Pilot 3000
You may wish to note that the Professor does maintain an office at Mars University, ...
His parents didn't call the police.
Fry: Aww. So you froze yourself to come look for me?
Michelle: No, I did it to get a fresh start. I didn't know what had happened to you -- no one did. The police were going to conduct a
search but your parents felt it was a waste of taxpayer money.
Fry: That's the same reason they kept me out of school. So, no one even ...
I. C. Wiener = "Icy Wiener" or "I See Wiener"
Wiener is a pretty benign slang for a penis. Something you might expect children to say. It works in the joke because it's also a fairly common last name. It can also be spelled 'weiner'.
In general, they both work.
In Futurama, the joke shows up when the main character delivers a pizza to a ...
Shout-out to Balok
This most certainly harks back to the Balok puppet based on the fact that, for at least one whole season of The Original Series, a still of the Balok puppet appeared in the closing credits of every episode, despite not appearing in those episodes:
Given the similarity of Kif's appearance, it seems they inserted him at an analogous ...
Professor Farnsworth may have started the company to fund his research (see Valorums answer), but he also sees it as cheap source of labor for his projects (similar to a research group in a lab):
Farnsworth: This is not a business. I always thought of it more as a cheap source of labor, like a family.
from Future Stock
Put here because I do not have enough reputation to comment on FryAmTheEggMan's comment above.
As a note, in a later episode (Law and Oracle IIRC) the employees at the cryogenics lab pull a similar prank on Fry, this time addressed to one "D. Frosted Wang". I think this heavily supports that the first meaning was the one intended by the writers. – ...
The Sexateria is not a real thing. By analogy with "cafeteria," the implication is that the Sexateria is a place where sex is purchased and enjoyed—presumably in the open, casual manner in which food is enjoyed at a cafeteria. (The joke is that this brothel has edged out e.g. the Wailing Wall as the must-see tourist destination of the 31st century's Holy ...
The pun here is that an "I.C Wiener" (I.C being a pun for 'icy' and wiener being a slang term for a penis) is found in a cryogenics lab, where people are frozen.
You may wish to note that in the original storyboards, the Cryogenics Lab was going to be a division of Birdseye, Inc., a company famed for its frozen products and the joke name on the slip was ...
By using the Dark Matter Engine
The Dark matter engine is the key to the extreme acceleration capabilities of the modern space ship.
Albert Einstein's famous statements that it would be mathematically impossible to travel faster than light seem to have held up throughout the 3rd millennia, and although in 2208 the scientific community allegedly raised the ...
The most noticeable one is right there in the first episode, immediately after Fry awakens in the year 3000. The cryogenic technician steps into the room and dramatically exclaims "Welcome to the World of Tomorrow!":
This seems to have been taken almost verbatim from the theme of the 1939 World's Fair, described by Wikipedia as "The World of Tomorrow", and ...
We have specific confirmation that Leela had sexual relations with;
Her ex-boyfriend Sean (the jazz-noodling imbecile)
Captain Zapp Brannigann (The "Velour Fog")
Delivery Boy 1st Class Philip J. Fry
Lars Fillmore ("Lars Lars and his fabulous jars")
Her former fiancée Alkazaar
Cubert J. Farnsworth (in an alternate timeline)
Lieutenant Kif ...
The other answers cover the main part of your question, but with respect to the techs in the cryo lab paying no attention to the new resident...
I think anyone who has been a "cog in the machine" employee would be able to tell you that nothing makes your life easier than the almighty shrug:
Tech 1: That tube was empty when I left yesterday.
Tech 2: Huh. &...
Because he's incredibly bad with financial decisions.
In the episode where Planet Express's stocks are being inflated by a 1980's businessman, he sells his stock in the company for a sandwich, fails to refrigerate it, and then eats it.
And in the series finale (the first time), he buys eight copies of a two-record set for no apparent reason, as well as ...
Typically you would pay upfront for cryogenic freezing. The fact that he falls into them on accident multiple times, leads me to believe that since he was already frozen the people running the place must have assumed he had already paid. (Billing never talks to the scientists; a typical lack of communication between departments)
The ship has dark matter engines that allow it to move faster than light. Also, remember that scientists increased the speed of light in 2208.
In the episode 'A Clone of My Own' the Professor takes Hubert outside of the ship to explain how it travels faster than light. At the end of the episode we see a demonstration of it as the space around the ship is ...
I think you might be reading into it too much.
He's literally (and figuratively) brainless because of the dumb things he did as the VP. Agnew was the only VP with criminal charges brought against him (extortion, bribery, tax fraud, conspiracy) he resigned to avoid the worst of it and later he publicly made anti-Semitic remarks.
We can see from the image below (from season 6) that Leela's skeleton is completely normal from the neck down. That would strongly imply that the bone that she's missing is within her skull or upper neck.
Presumably she's missing her nasal bone, since that would conflict with her big centrally-located eye.
In Season 1 episode 2 "I, Roommate" Bender leaves for the night, then after Fry decides to kick Bender out of the apartment, Bender stumbles into Planet Express the next day with a rust beard. The exact quote:
Leela: Look at that five o'clock rust. You've been up all night not drinking, haven't you?
Bender: Hey. What I don't do is none of your ...
I'd forgotten about James Sheridan's instance from the Radioactive Man episode, but I remembered another time that it popped up in Simpsons.
During the episode where they go to Itchy and Scratchy Land (Season 6 Episode 4), Bart is looking for a personalized license plate, and there is no space for "Bart", but they're sold out of "Bort" plates.
This would ...
"Wiener" is a silly slang word for penis — it's often spelled "weiner", because elementary school kids aren't so big on spelling and it's not like they're gonna ask their teachers for correction — but it's spelled "Wiener" in the episode:
There are dozens (hundreds?) of slang words for male anatomy, but this one is pretty easy to trace. "Wiener" is from ...
I think you may be confusing poodles (a breed of dog) with all dogs;
Farnsworth: Pine trees have been extinct for 800 years, Fry. Gone the way of the poodle and your primitive notions of modesty. Ah!
Futurama: Xmas Story
As has been noted in the other answers, dogs of other breeds do appear in later episodes.
Futurama: The Day the Earth Stood ...
I had thought vaguely that "Crimes of the Hot" had stated robots were invented by
Professor Farnsworth, but I just watched the episode again and he actually says..
(That is the last 'spoiler warning' I am including - the rest is basically spoilers..)
Note that Bender is provably older than most robots. Not only did he get sent back
to 1945 in "All's well ...
Probably for the same reason airplanes today still have pilots:
People, as a general rule, don't trust machines.
Pilots are likely still around to assuage the anxiety people might have about trusting their lives (or livelihoods) to a machine, even if in actuality the machine is doing all the actual piloting.
Moreover, having a pilot around can be useful ...
To answer this, it's important to understand how carbon dating works.
Basically, when plants photosynthesize, a certain percentage of atoms they get in CO2 from atmosphere are unstable C14 isotope. They get incorporated in the plant tissues, and the percentage of C14 there gets roughly the same as in the atmosphere. You eat the plants or you eat the animals ...
The closest I've seen is a canon quote from Moby Dick that seems hauntingly similar;
So in dreams, have I seen majestic Satan thrusting forth his tormented
colossal claw from the flame Baltic of Hell. But in gazing at such
scenes, it is all in all what mood you are in; if in the Dantean, the
devils will occur to you; if in that of Isaiah, the ...
To the best of my knowledge this is never addressed on screen.
Off-screen, either Al Gore or the Nibblonians took care of the costs.
Both groups are fully aware that the fate of the entire universe depends on Fry remaining frozen at the cryo-centre. Neither group seem to lack the funds to ensure that this takes place.
Off-screen, Fry took ...