OK, this was an Air Force one a few years back but my unit is a sub unit for a bigger wing elsewhere so we regularly got phone calls from admin people we didnt know. We had a not too bright guy and played a prank on him. He came into the office and we gave him a note with just a phone number on it. Told him "Captain Deies from the 165th called and wants you to call him back immediately." He picked up the phone and called and was answered. From our end we heard "Yes sir this is Senior Airman XXX, you were looking for me?" pause "I have a note here that says I was supposed to call you" pause..... at that point too many people were cracking up for the guy not to get it. We gave him the number for Captain D's seafood. Post some more after lunch.
post lunch: Lets see, The Air Force in my field has a lot more admin type jokes. We had a guy who left his computer unlocked when he walked away so we jumped on there and sent our shop chief an email. Not just any email. It was a homoerotic star wars email/admiration email. Everything from stroking a wookie to handling light sabers and how much he loves being under the chiefs authority. Well we hit send right before he entered the office again and the chief was in his office across the hall. We told him to go knock on the glass and wave to let the chief know he was there. Watching someone in charge snort out hot coffee is highly under rated.
When we were working with chemical warfare gear one time, checking it over and making sure the parts were in good working order, the same guy from the first prank was present. One of us asked him if he had a Strap-on for his mask(he wasnt the sharpest tool in the shed). He said no of course. So we sent him to ask the chemical weapons guy(the guy was an ex NFL player and had a dry but evil sense of humor

) if he could get a strap on. Well a little while later we got a phone call from him and a slight chuckle telling us "we were so wrong." He told the guy he didnt have any and to go to Supply and ask. No phone calls from supply but they played into it and sent him back to our office to ask our shop chief. We could hear the chief's laughter from upstairs before he yelled at us to quit sending people on wild goose chases, it wastes too much time.
When I was in the army we were at a small rifle range in Korea zeroing our Aim Points(a scopelike thing that doesnt magnify vision but presents a holographic red dot where the bullet will go.) There were only like 4 or five lanes and 150 of us to use them so there was a ton of downtime being bored. So what do army infantry people do when we are bored, we mess with people. In basic training we all used this series of radio equipment with the acronym PRC with an accompanying number for the model , and normally acronyms get shortened to a word, in this case "Prick-##" . So what is probably the oldest trick in the army since the invention of the PRC series of radios, send the new guy looking for one. We had a guy who was relatively new to the military and our squad leader an E-6 sent our new guy to the platoon leader, who was an E-7, to look for a "Prick E7". With a straight face he said he didnt have one, so he told him to go ask the 2nd platoon sergeant and went with him, shaking his head at us. We saw nearby the 2nd plt sergeant smile and assume he didnt have one either so he sent him to 1st platoon. 1st Platoon's sgt lacked a sense of humor and immediately stalked over to us for a 30 minute push-up session. It was still funny.
At Benning, our First Sergeant was this absolute PRC redneck(I am from GA, I am allowed to say it, besides its easier to picture the guy with that description) with a beat up Ford pick-up truck. Someone found it funny one day to put a gay pride rainbow decal on his bumper. There is stood for 3 days until either he noticed or someone told him. He had the entire company outside demanding the guilty party and smoking us(making us do muscle exhausting exercises like pushups and grass drills) until someone talked. No one did. And for almost an entire after noon we got really dirty and tired. It was still funny.
Same unit in the deserts of the Middle east. My unit had 1st response guard duty for a two week rotation. I was in the tower with a machine gun overlooking the front gate of the base. At the front wall(there was a double wall with about a hundred yards of open sand in between) was the actual gate guards who inspected incoming vehicles. Below my tower was a Bradley fighting vehicle also covering the front gate with its 25mm chain gun. They got bored in the middle of the night and all of a sudden I hear "BANG!" and then "Bang!", and then over and over again. I look down to see the driver beating on various places of the armored vehicle with a sledge hammer and from the ground he couldnt see the gunner and vehicle commander cracking up in the turret. This continued for about 15 minutes until a staff duty person from the MRLS artillery battery across the dirt road behind us walked up and stopped the hammerer. He yelled at the Bradley commander that the Battery commander said "He appreciates the diligence to detail the crew is showing making sure the vehicle is up to spec but to please have his driver look for weak spots in the armor in the morning after everyone is awake."
Oh and a tragic but still funny moment, in my current unit a good 6 or 7 years ago a senior ranking NCO sent an off color joke by email to a few people. They try to stress political correctness and such in the military, but frankly, the military prides itself on the lack of in defiance, so this isnt unusual. Well I never got to read this joke to see if it was funny as it was removed from the system by someone higher than me. However this was not before every person he didnt want to read it, read it. He using the wonders of Outlook addressed the email instead of the group he wanted, to the next group down which was every member of every shop of the same type he was in in the entire Air Force and conveniently enough, he had a signature with his and the unit's DSN phone number at the bottom. So as the world turned and people showed up for work and diligently checked their emails, they had a surprise waiting for them, and every half hour the unit got calls from commanders and shop chiefs in new time zones. He was asked to retire and had the quickest paperwork process I have seen. He was young enough so he went to work for the city police department. We thought it was funny.