Life, the Universe and Everything provides examples of the following Tropes:
Absolute Xenophobe: The Krikkiters were so isolated and convinced that they were alone in the universe that instant they discover that there is more of the universe beyond Krikkit, they decide "It'll have to go." Of course, the circumstances were arranged by Hactar so they'd reach that conclusion.
Affably Evil: The Krikkiters are intelligent, charming, whimsical people who have a strong sense of family, regularly sing phenomenally beautiful songs, and believe in the obliteration of all other life forms.
Apocalypse How: The entire galaxy at first is under risk, until the Krikkitmen raise the stakes by targeting the whole universe.
Bored With Insanity: While trapped on prehistoric Earth, Arthur calmly decides to go mad, and then Ford pops up and cheerfully claims that he went mad for a while and pretended that he was a lemon. It gets weirder from there.
Brick Joke: In true Adams spirit, an incidental anecdote proves vital to saving the universe. Similarly, the bowl of petunias back in the first book.
Bunny-Ears Lawyer: Judiciary Pag, LIVR (Learned, Impartial and Very Relaxed), is an obvious cad, but because he has the finest legal mind in history he more or less gets away with calling two grillion fatalities "a whole lot of stiffs".
Cerebus Retcon: That funny incident about the bowl of petunias in the first book is a lot less funny when the reason behind it is explained here.
Chekhov's Armoury: In the first few chapters alone, Arthur's rabbitskin bag, a Chesterfield sofa, a cricket ball, the Ashes, and a man with a weak heart condition appear. All of them will reappear later, with greater significance.
Cosmic Plaything: Agrajag, a being who is repeatedly reincarnated and then killed by Arthur Dent. Agrajag is driven mad by his own repeated murders.
The Dreaded: The Krikkitmen are known and feared throughout the rest of the galaxy for waging the bloodiest war in history. Their alarmingly efficient Krikkit robots are depicted as even more fearsome than they are.
Expy: The whole story began its life as a Doctor Who screenplay (Doctor Who and the Krikketmen), so some of the characters are reimagined as expies of Doctor Who characters. For example, Slartibartfast is an expy of the Doctor, Arthur Dent and Trillian are both expies of the Doctor's companion(s).
Gotta Catch 'Em All / MacGuffin: The three pillars and two bails of the Wikkit Gate, which the Krikkit robots (and Slartibartfast) are searching for.
Hair-Trigger Temper / Feeling Oppressed By Their Existence: The Hitchhiker's Guide to the Galaxy says that the best way to pick a fight with a Silastic Armorfiend of Striterax was just to be born. They didn't like it, they got resentful. And when an Armorfiend got resentful, someone got hurt.
Knows A Guy Who Knows A Guy: Effrafax of Wug got rid of the mountain he was supposed to render invisible with the aid of "his friends, and his friends' friends, and his friends' friends' friends, and his friend's friends' friends' friends, and some rather less good friends of theirs who happened to own a major stellar trucking company."
Lovable Coward: Ford argues with Slartibartfast more than once over whether they should try to stop the white robots or go to a party, drink a lot and dance with girls. Ford, naturally, favours the latter option.
Near Villain Victory: The last third of the story largely resolves around the heroes trying to prevent the Krikkitmen from going through with their plans for universal destruction, and at times they come perilously close to failing.
Newspaper Dating: How Arthur finds out what day it is when he appears in Lord's Cricket Ground.
Norse Mythology: At the party, Thor tries putting the moves on Trillian, much to Arthur's annoyance.
Obliviously Evil: Possibly the Krikkitmen, who, having lived on the planet Krikkit in isolation of the rest of the galaxy for several eons, naturally reacted badly to news that the rest of the universe exists. Later, this is subverted, but in an unexpected way.
Puff of Logic: When flying, it is vitally important not to say things like "I can't possibly be flying", or else you will turn out to be correct.
Shout-Out: The wildest party in the universe - which owing to the intervention of some second-generation astro-engineers, now flies drunkenly over the surface of a planet which it periodically raids for more booze and munchies - mirrors Jonathan Swift's creation of the floating city Laputa, which also produces nothing of its own and acts as a parasite, periodically descending to Earth and taking what it needs by force.
Sound Defect: In the BBC Radio 4 adaptation, the insertion of the key into the Slo-time lock is interrupted by the Guide, which digresses on the subject of sound effects and why that one didn't "cut the mustard" before substituting a second sound effect.
Space Clouds: The Krikkit people have never seen stars and are entirely unaware of the night sky specifically because their planet lives inside a cloud of Hactar's debris.
Suicidal Cosmic Temper Tantrum: The people of the planet Krikkit live on a planet surrounded by a totally opaque dust cloud, so for centuries, they knew nothing of the universe beyond their planet and the star they orbited. When a spaceship crash-landed on the planet, they used it to take an exploratory trip, curious of where it came from, and saw the universe for the first time. Their immediate reaction? "It'll have to go." This becomes doubly important later, when Arthur, Ford, Slartibartfast and Trillian head down to the planet itself and learn about the supernova bomb.
Take That: The Running Gag about Paul McCartney, noting that the royalties from even a single Macca song would enable him to buy first a medium-sized town, then the whole of Hampshire (one of England's most affluent counties) and finally, should Macca hit on a theme half as lovely as the one hummed by the Krikkiters, escalating to ownership of massive swathes of the South of England. This derives from performing rights issues for the LP version of H2G2, where Trillian faces death and oblivion whilst humming A Day In The Life. McCartney's copyright lawyers hammered Adams and his production company for serious money, for the use of just two bars of a Beatles' song. Sung by somebody else. Adams worked this experience of being fleeced into this novel.
Temporal Paradox: The Campaign for Real Time largely seems to consist of trying to stop these paradoxes from happening. At the climax, the future of the galaxy hinges on whether or not one of these is possible.
Took a Level in Badass: Arthur, being the Unfazed Everyman, takes the next step in his Character Development and stands up to a thunder god (and lives). Trillian goes from being a passive bystander to being an important character, and works out the mystery of what was really going on before the Krikkit Wars began.
Weirdness Censor: The "Somebody Else's Problem" Field will hide anything sufficiently unexpected, inexplicable or disturbing.
Ford: I told you! Eddies in the space-time continuum!
Arthur: And this is his sofa, is it?
Who Wants to Live Forever?: Wowbagger the Infinitely Prolonged, initially enjoys immortality, but eventually gets bored and resentful of mortals, so he finds an unusual way of coping with his predicament.
Why Isn't It Attacking?: Zaphod is repeatedly shot and beaten around the heads by the Krikkit robots, but not killed, which is stated as being unusual behaviour for the robots. The reason is that Marvin prevents them from doing so via the motherboard computer.
Unsound Effect: The materialisation and dematerialisation of a Krikkit warship literally sound like several thousand people simultaneously saying "wop" and "foop", respectively. Both of these are common sound effects reversed.