Here are some jokes from the GDR that I've translated.
Q: Why do the People's Police go out on patrol in groups of three? A: One can read, one can write, and the third is there to keep an eye on the two intellectuals.
Judge Schnauz walks into the cafeteria of the Erfurt district court bent over with laughter. Other judges and lawyers ask him why he is so amused. "Oh, comrades, I've just heard the latest political joke!" "Tell it to us!" "Unfortunately, I can't do that. I've just sentenced a barber to two years of prison for it!"
In Eisenach (home of the IFA Wartburg car factory) they heard about how the Japanese test a car. They put a cat in the car, and if after three days the cat is dead, the parts are judged to be close fitting. Not wanting to be second in anything, the people in Eisenach decided to test the Wartburg in a similar fashion. If after three days the cat is still in the car, the parts are judged to be close fitting.
The leader of the GDR, Erich Honecker, wants to know what the people really think of him. So goes out among the people in disguise. He asks a man on the street: "Excuse me, but what do you think of Honecker?" The man leads him down a side street, makes sure that nobody hears him, and whispers into Erich's ear, "I support Honecker!"
Erich Honecker receives a gold watch for his birthday that he is very fond of. He even keeps it under his pillow when he goes to bed. One day, while at the office, Erich realizes that he is missing his watch. In a panic, he calls Erich Mielke (the head of the Stasi) and tells him that someone has stolen his watch. Later, he realizes he left it under his pillow, and being relieved, calls Mielke to tell him to cancel the investigation. Mielke responds "Too late, we've arrested three suspects and they've confessed everything!"
Two inmates in the Bautzen political prison are talking about their sentences. "How long are you in for?" "Five years." "And what did you do?" "Nothing." "Can't be. For nothing you get ten years!"
Erich Honecker is on a diplomatic mission in Austria. Various government ministers of the GDR and Austria are introduced. Finally, a man is introduced as the Minister of the Austrian Navy. Honecker bursts out laughing: "But you have no coastline!" The Austrians are offended. "We were very polite when the GDR's Minister of Trade was introduced!"
Two soliders are patrolling the Wall, looking westward: "What are you thinking of when you see the enemy state of our homeland?" "The same as you are." "Then, unfortunately, I must arrest you!"
Wherever a comrade is, there is the Party. Wherever 50 comrades are, there is an Intershop.
("Wherever a comrade is, there is the Party" was the Communist Party slogan. Intershops were special stores that sold hard to get goods in exchange for Western currency. In practice, only high ranking Party members and Western tourists could shop there.)
Erich Honecker wakes up, throws open his doors and welcomes the rising sun with a hearty "Good morning." "Good morning, dear Erich," it replies. After lunch he greets the sun again. "Good day, dear Erich," it responds. At bedtime he bids the sun goodnight. "Kiss my ass," it tells him. "I'm in the West now."
The Trabant (or Trabi, as it was nicknamed) was the most common car in the GDR, and its lack of power and general unreliability made it the target of many jokes. Some examples follow:
Q: When does a Trabi reach its top speed? A: When it is towed away.
Q: How do you measure the acceleration of a Trabi? A: With a diary.
Q: Why do some Trabis have heated rear windows? A: To keep your hands warm while pushing!