The entire "whale and petunia falling to the planet" sequence.
"I wonder if it'll be friends with me?"
"Curiously enough, the only thing that went through the mind of the bowl of petunias as it fell was, 'Oh, No... Not Again!'. Many people have speculated that if we knew exactly why the bowl of petunias had thought that we would know a lot more about the nature of the universe than we do now."
Arthur and Ford imprisoned in the Vogon ship.
Arthur: It's at times like this I wish I'd listened to what my mother told me. Ford: Why, what did she tell you? Arthur: I don't know, I didn't listen.
Ford being an utter troll a few seconds earlier counts as well...
Arthur: So this is it, we're going to die.
Ford: Yes... but. No. Wait a minute! What's this switch!?
Arthur: Where!? Where!?
Ford: No, I was only fooling. We are going to die after all...
And of course the scene with Zaphod and the Total Perspective Vortex. "Hey, is that a piece of fairy cake?"
"If I told you how much I needed this," he said ravenously, "I wouldn't have time to eat it." He ate it.
Oolon Coluphid's Trilogy of Philosophical Blockbusters: Where God Went Wrong, Some More of God's Greatest Mistakes and Who is this God person anyway?
Well, That About Wraps It Up for God.
In the beginning, the Universe was created. This has made a lot of people very angry and been widely regarded as a bad move.
"They found only an old man who claimed that nothing was true, although he was later discovered to be lying".
Ford: That's beside the point! The point is that I'm turning into a "perfectly safe" penguin, and my colleague here is rapidly running out of limbs! Arthur: Oh, that's all right, I've got them all back now...admittedly, they're a little longer than I'm used to.
Ford trying to retain his intellectuality and explain the universe while hammered!
*gigantic tank-shaped robot rumbles into view and demolishes nearby building with its tracks*
Zaphod: Holy photon, what's that?
Hitchiker: A tank. Frogstar scout robot class D come to get you.
This bit becomes even funnier in the radio version, where it's revealed that the scout robots actually knew Zaphod was there, and called the Frogstar tank to get him.
Second: Marvin has been left alone with no weapons to deal with this tank-robot. After a long guessing game in which the tank tries to discover what they've armed Marvin with to stop him, he finds out they didn't give him anything.
Marvin: I'll tell you what they gave me to protect myself with shall I?
Tank: Yes, alright.
Marvin: Nothing at all, not an electronic sausage.
The tank, after ranting some more, decides to take out his anger:
Tank: I think I'll smash the wall down! *does so* I think I'll shoot down their bloody ceiling as well! *does so*
Marvin: That's very impressive.
Tank: You ain't seen nothing yet, I'll take out this floor too, no trouble! *does so... and falls down*
Tank: Hell's bells! *smashes itself to bits on the ground fifteen stories below*
"For a moment, nothing happened. Then, after a second or so, nothing continued to happen."
From the Secondary Phase, the book describes the motto of the Sirius Cybernetics Corporation Complaints Department, "Share And Enjoy", and brings up how the company song is sung on special occasions by a choir of robots. Unfortunately, due to the expected malfunctions, the robots sing a flattened 5th out of tune. Hilarity Ensues, both in tonal dissonance and in utterly bizarre lyrics.
This little exchange:
Ford: How do you feel? Arthur: Like a military academy. Bits of Me Keep Passing Out. [pause] Arthur: If I asked you where the hell we were, would I regret it? Ford: We're safe. Arthur: Oh good. Ford: We're in a small galley cabin in one of the spaceships of the Vogon Constructor Fleet. Arthur: Ah. This is obviously some strange usage of the word "safe" I wasn't previously aware of.
"We're going to get lynched, aren't we?"
"Vell, Zaphod's just zis guy, you know?"
A clever joke that you probably didn't get the first time round:
Ford: It's unpleasantly like being drunk. Arthur: What's so unpleasant about being drunk? Ford: You ask a glass of water.
Specific to the TV series
The illustration that pops up when the Guide says, "Most leading theologians claim that this argument is a load of dingo's kidneys..."
During the entry on Vogon Constructor Fleets, the visuals during the last part.
First, "The best way to get a drink from a Vogon is to stick your finger down his throat..."—image is simply text to the effect of "It's too disgusting to show you".
Second. "...and the best way to irritate him is to feed his grandmother to the Ravenous Bugblatter Beast of Traal." First it shows the same images of the Vogon grandmother and the Beast from earlier in the entry, then it shows the latter actually eating the former.
Specific to the books
The Hitchhiker's Guide to the Galaxy
Oh sweet Jesus, everything. Just in the first few pages there's the bit about the word 'bulldozer' going through Arthur's head, Arthur in the mud, Genghis Khan, putting a bag over your head when the world is ending . . . trying to describe it all would barely be shorter than simply posting the entire thing.
The foreman in the first book, who is distantly descended from Genghis Khan and repeatedly has urges to go tearing around the countryside doing the standard maim pillage burn routine.
"...with two large axes crossed over the front door. His wife wanted hanging roses, but he wanted axes. He didn't know why, he just liked axes."
This bit of dialogue a fantastic commentary on the human condition, and is delivered absolutely perfectly in the television version.
"I'd rather be happy than right."
"And are you?"
"No. That's where it all falls down, of course."
The feelings that Deep Thought has for other computers. "The Milliard Gargantubrain?" said Deep Thought with unconcealed contempt. "A mere abacus - mention it not."
"Molest me not with this pocket calculator stuff!"
And then it claiming a few seconds later, on the subject of another supposedly 'Great' Computer:
Deep Thought: The Great Hyperlobic Omnicognate Neutron-Wrangler can talk all four legs off an Arcturan Mega-Donkey, but only I can persuade it to go for a walk afterwards.
The Restaurant at the End of the Universe
"In the beginning the Universe was created. This had made a lot of people very angry and had been widely regarded as a bad move."
In the second book, The Heart of Gold was being attacked by a Vogon ship and they couldn't move because the ship computer was too busy trying to make tea. The force-shield started blistering and cracking under the sudden, unexpected attack. Ford thought it would probably hold for about four minutes...
"Three minutes and fifty seconds," he said a short while later.
"Forty-five seconds," he added at the appropriate time. He flicked idly at some useless switches, then gave Arthur an unfriendly look.
"Dying for a cup of tea, eh?" he said. "Three minutes and forty seconds."
"Will you stop counting!" snarled Zaphod.
"Yes," said Ford Prefect, "In three minutes and thirty-five seconds."
The original version of that exchange (in the radio program) was also hilarious:
Arthur: I'm sorry, it's just that I was dying for a cup of tea!
Zaphod: You soon will be, baby!
The Dangers Of Teleportation
I teleported home one night
With Ron and Sid and Meg
Ron stole Meggie's heart away
And I got Sidney's leg.
The first thing that hit their eyes was what appeared to be a coffin. [pause] And the next four thousand nine hundred ninety-nine things that hit their eyes were also coffins.
The Golgafrinchans are fairly stupid, but the Captain is absolutely hilarious.
Number Two: Sir! They are trespassing on the ship!
Captain: Oh, I expect that they probably just dropped in for a quick jynnan tonnyx, don't you, Number Two?
And then later...
Number Two: May I remind you... that you have been in that bath for three years?!
The discussion about jynnan tonnyx, in which Adams manages to top the Pan Galactic Gargle Blaster routine from the earlier book, telling how each civilisation in the galaxy has a drink whose name has the same phonemes, from "jinond-o-nicks", which is "ordinary water served at slightly above room temperature", to "Tzjin-anthony-ks", which "kills cows at a hundred paces".
All you have to do is deposit one penny in a savings account in your own era, and when you arrive at the End of Time the operation of compound interest means that the fabulous cost of your meal has been paid for. This, many claim, is not merely impossible but clearly insane
Life, the Universe and Everything
The whole "Eddies in the space-time continuum." confusion is hilarious.
Ford's elaboration on his temporary madness right before it is even better.
Arthur: I thought you must be dead... Ford: So did I for a while, and then I decided I was a lemon for a couple of weeks. I kept myself amused all that time jumping in and out of a gin and tonic. Arthur: Where did you...? Ford: Find a gin and tonic? I found a small lake that thought it was a gin and tonic, and jumped in and out of that. At least, I think it thought it was a gin and tonic. I may have been imagining it.
And the brief return many chapters later:
Slartibartfast: Eddies in the space-time continuum you see.
Arthur: So I hear.
"There is an art, it says, or rather, a knack to flying. The knack lies in learning how to throw yourself at the ground and miss."
"...except for your sudden obsession with whelks."
The entire Agrajag sequence is quite possibly the funniest segment ever put to prose.
Not to mention the fact that it is the punch line of the funniest Brick Joke in literature.
Made even funnier in the audiobook, due to Agrajag being a Large Ham.
The conversation between the cricket commentators about "mysterious materialisations on the pitch", to anyone who has heard "Test Match Special" on the radio it sounds like exactly how they would react to such a situation.
"Well the supernatural brigade are certainly out in force", burbled a radio to itself.
The conversation with Murray Bost-Henson, a tabloid journalist, and his revelations that the "Rain God" trucker is real ("Do you know how much they're paying this guy not to go to Malaga this summer?"), that Arthur actually sent him to the papers in the first place - he suggests Arthur pose under a hosepipe as the "man who made the rain god rain", and the "Week of the Weirdos" segment about the mysterious flying couple (see above).
The 'chronicler' Breaking the Fourth Wall and addressing the reader directly, possibly after being asked too many questions about Arthur Dent's personal life, is a hilarious strop on Douglas Adams part:
"This Arthur Dent" comes the cry from the furthest reaches of the galaxy, and has even now been found inscribed on a mysterious deep space probe thought to originate from an alien galaxy at a distance too hideous to contemplate, "what is he, man or mouse? Is he interested in nothing more than tea and the wider issues of life? Has he no spirit? has he no passion? Does he not, to put it in a nutshell, fuck?"
Ford deliberately running up huge expenses as a restaurant critic, culminating in trying to charge the purchase of London Zoo and the entire hotel he is staying in to room service.
This quote early on in the book:
The Hitch-Hikerís Guide to the Galaxy has, in what we laughingly call the past, had a great deal to say on the subject of parallel universes. Very little of this is, however, at all comprehensible to anyone below the level of Advanced God, and since it is now well-established that all known gods came into existence a good three millionths of a second after the Universe began rather than, as they usually claimed, the previous week, they already have a great deal of explaining to do as it is, and are therefore not available for comment at this time.
The fate of the history faculty of the University of Maximegalon:
When the Infinite Improbability Drive arrived and whole planets started turning unexpectedly into banana fruitcake, the great history faculty of the University of Maximegalon finally gave up, closed itself down and surrendered its buildings to the rapidly growing joint faculty of Divinity and Water Polo, which had been after them for years.
And Another Thing...
Whatever else you may have to say about And Another Thing, most of the business with the cows desperate to be eaten were pretty funny, especially the "I'll track down your entire family and not eat them!" bit.
The Guide: The standard repository for all knowledge and wisdom in the universe is called The Hitchhiker's Guide to the Galaxy, and it has this to say about movie trailers.
Movie trailers are designed to give you an idea of the film in question in a very short space of time. [footage of Arthur waking up to find the bulldozers about to demolish his house] Typically, they begin with the introduction of a main character, who will very shortly have something utterly fantastic happen to him, that someone just had to make a movie about it. Often, this section is preceded by the words "In a world"....[Earth explodes]....but sometimes not.
Trailers also normally employ A DEEP VOICE that sounds like a seven foot tall man who has been smoking cigarettes since childhood.
The goal is to create a piece of advertising that is original and exciting, yet intelligent and provocative. In other words: lots of things blowing up. [cue montage of explosions from other movies] Occasionally interrupted by a girl in a bikini.
The airlock scene has an awesome moment of false hope being crushed for laughs: "So this is it? We're going to die?" "Yea, we're going to . . . No, no what's this? This . . . this is nothing; we're going to die."
"Ford?" "Yes?" "I think I'm a sofa." "I know how you feel." AHHHHHHH!!!!!
Also, the scene where after using the improbability drive, everyone is animated as yarn dolls, then Arthur vomits as we return to live action, with one yarn thread sticking out of his mouth.
The Overly Long Gag of the camera jump-cutting into outer space while Ford is holding onto Arthur and trying to hitch a ride on a Vogon ship and Arthur is screaming bloody murder before Earth is destroyed by the Vogons.