It’s how the Romans got their water.
Vladimir and Estragon are standing out in the water for so long their legs get wrinkled. Finally Estragon’s sister comes up and asks them why. She is told they are wading for Godot.
::: slow solitary clap, builds to a deafening roar of multitudes cheering :::
Not sure if this counts as absurdist, but this is one of my favorite jokes:
It’s business as usual for a bartender, and one day as he is cleaning his bar when an unusual customer walks in. The man is dressed in an expensive suit, has a beautiful supermodel hanging off each arm, and has a limo parked outside. Furthermore, the man has an orange for a head.
The customer sits down at the bar and orders everyone a drink. He pays for it from a roll of hundreds and manages to get the attention of every woman in the joint, despite having an orange for a head.
The bartender is not a man to pry, but he feels compelled to ask about this man’s life.
“Excuse me,” says the bartender, “I can’t help but notice that you’re obviously fabulously wealthy and irresistable to women, but you have an orange for a head. How did that happen?”
So the man told his story.
"A while back, when I was penniless, I was walking along the beach and saw an old lamp, half buried in the sand. I picked it up and gave it a clean, and POOF! out popped a genie. The genie explained that he had been trapped in that lamp for two hundred years, and that he was so grateful to me for freeing him that he would give me three wishes.
"For my first wish I asked for an unlimited fortune. The genie said ‘It is done!’ and from then on, whenever I needed money, it was there.
"For my second wish I asked for the attention of all the most beautiful women in the world. The genie said it was done, and since then I have been able to get any woman I wanted.
“For my third wish – and, this is the bit where I kinda fucked up – I asked for an orange for a head.”
*What’s the difference between a duck?
That’s a riddle that makes no sense
If someone happened to ask you that
You’d think them rather dense
But if you don’t know the answer
Then you’ve only yourself to blame
The difference between a duck
Is one of its legs are both the same*
— Riddles, a British pop song from 1932
Riddle me riddle me ree
Riddle me riddle me roo
We’ve got the riddles
And the answer’s up to you
What’s the difference between absurdist humor punchline and a random word lookup table?
–
In the spirit of randomness, Rowlf the Dog sings Cottelston Pie!
You try to cross that road a-chicken, and you’ll find out!
The following may not be what you’re looking for and in event is very old and well known … but I still like it. 
-
How do you put a giraffe into a refrigerator?Correct Answer: Open the refrigerator, put in the giraffe, and close the door. This question tests whether you tend to do simple things in an overly complicated way.
-
How do you put an elephant into a refrigerator?[SPOILER]Did you say, Open the refrigerator, put in the elephant, and close the refrigerator?
Wrong Answer.
Correct Answer: Open the refrigerator, take out the giraffe, put in the elephant and close the door. This tests your ability to think through the repercussions of your previous actions.[/SPOILER]
3. The Lion King is hosting an animal conference. All the animals attend… except one. Which animal does not attend?Correct Answer: The Elephant. The elephant is in the refrigerator. You just put him in there. This tests your memory.
Okay, even if you did not answer the first three questions correctly, you still have one more chance to show your true abilities.
- There is a river you must cross but it is used by crocodiles, and you do not have a boat. How do you manage it?
Correct Answer: You jump into the river and swim across. Have you not been listening? All the crocodiles are attending the Animal Meeting. This tests whether you learn quickly from your mistakes.