The following, although short is funny enough that several people I know demanded I turn it into an article. This is all true, and is filed in a report I recently read.
In 1936 a British military mission was heading to Russia to observe manoeuvres at Minsk. It consisted of General Wavell (better known for his time in the desert in 1940, and then in Burma), Lieutenant General Martel (the famous British tank officer and engineer, also commanded the British forces at Arras) and a Major Hayes. The Air Force was represented by Wing Commander Wigglesworth.

To get to these manoeuvres they travelled via Berlin where they met Colonel Hotblack, who won a DSO in the First World War. He had a background in reconnaissance and intelligence and spoke fluent German. Col Hotblack was the lead military attaché to the Berlin embassy, over dinner he entertained his guests with a recent occurrence in the German Army.
Hitler is confused!
Apparently the Germans kept on receiving reports of British inefficiency. This confused Hitler greatly, because despite the inefficiency the British armed forces carried on succeeding. Obviously he wanted to find out how the British achieved this, and apply it to their army to make it more efficient. To this end Hitler ordered an inquiry into the subject. After its deliberations the German inquiry came to the conclusion that it was the British sense of humour that was responsible.

And so, somewhat predictably Hitler decreed that the Germans should try to install a British sense of humour into the German army, only they did it in a very German way. First they tried to teach jokes by numbers. You'll never guess what, that plan failed miserably.

So undeterred they tried a new approach. The idea was to let the soldiers soak up the humour naturally. So they took a number of Bruce Bairnsfather's cartoons (creator of the "if you know of a better hole" cartoon) and translated the jokes directly into German. Every week a new poster would be displayed in all the barracks across the German Army. Col Hotblack asked if he might view the first trial carried out by the Germans, which the Germans happily agreed to.
The cartoon selected for the first German trials.
When Col Hotblack arrived he found the German translation of the poster, only at the bottom the Germans had had to add another line, to explain the joke. In this case the German addition read "Of course the hole was not really made by a mouse at all!"
With a straight face Col Hotblack stood aside and the first unit of Germans were marched, turned to face the poster, and ordered to read the writing so they might absorb the British humour. After they had dutifully done so, they were marched out. Not one of them had so much as smiled.

Would you like to know more?

There is one other incident about German Army humour. They did try again 73 years later in Afghanistan, putting this t-shirt on sale on German Army bases.
Nope, can't see how this will go wrong...
It references the 2009 Kunduz airstrike. When it was reported in Germany there was a total and utter sense of humour failure on behalf of the German politicians and German high command. The German regional high command ordered the t-shirts to be removed from sale, banned their wearing, and launched an investigation into the t-shirt. They promised if any German soldiers had been involved in the design or manufacture they would be brought up on disciplinary charges.

However the German soldiers tried again with another t-shirt. This one read “My Grandpa never got this far east!”. Looks like the German army finally deployed humour!