Only two pages in and the Discworld series immediately establishes what it's going to be full of: semi-relevant anecdotes (in this case, a discussion on the World Turtle A'Tuin) with a So Bad, It's Goodpunny joke at the end (the big "bang" theory).
Rincewind trying to swear at Twoflower in Trobian, which doesn't really have profanities:
You little [such a one who, while wearing a copper nose ring, stands in the bath atop Mt. Raruaruaha during a thunderstorm and shouts that the goddess of lightning has the face of a diseased uloruaha root]!!
Rincewind working out the meaning of several words Twoflower uses, like "tourist":
Twoflower was a tourist, the first ever seen on the Discworld. Tourist, Rincewind had decided, meant "idiot".
"Some pirates achieved immortality by grand deeds of cruelty or derring-do. Some achieved immortality by amassing great amounts of wealth. But the Captain had long ago decided that he would, on the whole, prefer to achieve immortality by not dying."
The competing theories about the nature of the universe: the Steady Gait (as opposed to our world's Steady State theory of Fred Hoyle) and the Big Bang hypothesis - which, as it involves turtles mating, is the other meaning of 'bang'...
The 2008 TV film
Rincewind attempting suicide by jumping off the docks is sad an all, but it immediately becomes funny when he's saved by a rising platform... And then it becomes hilarious when we suddenly cut to Death nearby who grumbles at the man's survival.
Death: ...Disappointing.
When Rincewind and Twoflower are meeting for the first time they are discussing the Counterweight Continent.
Rincewind: But the legend says it's made of gold.
Twoflower: Well, it's not made of gold. Gold is just a really common metal there.
Rincewind: You might like to keep that to ourselves.
(Rincewind turns around and sees Broadman several inches away from his face)
Rincewind is trying to drag Twoflower out of Death's house. Then we get this exchange:
Twoflower: Amazing! I've never been at Death's door before!
Rincewind flipping off Broadman and Blind Hugh after succeeding in communicating with Twoflower.
In a deleted scene, Trymon is shown hiring Herenna to bring back Rincewind. Herenna asks if Rincewind is like all wizards, long-robed smokers. Trymon states the contrary: Rincewind is scruffy, incompetent and can't even spell the word "wizard". Herenna has a hilarious look of disbelief on the last remark.
David and Sean, tied together, try to stand up... and the rope breaks.
Lord Vetinari getting Rincewind's name wrong.
Rincewind tries to bail on Twoflower, but forgets his hat.
David drawling, "Yes, you try it, love, I've already sorted a girl out."
In another deleted scene, Rincewind uses reverse psychology to get Twoflower to come to Ankh-Morpork with him and can't help but insult Twoflower while doing so.
Rincewind: Anyway, following me only guarantees the risk of death. Or was it following you? I can't remember.