Ok, I’ve heard JARHEAD for the marines, KNOB for a Citidel freshman, and somewhere there is SCRUB, althugh, I’m not sure who they are.
What are some more ? Are they considered derogatory by the subjects?
Call a Navy man a Squid and see what happens.
navy = swabbies
army = grunts
air force = flaps
Some of these might be somewhat dated but: “Grunt” for infantryman, “swabie” (or “swab jockey” or “swab”) for a sailor, “birdman” (or “junior birdman”) for a member of the air force.
“Top kick” for first sargent, “lewie” for a lieutenant, “shave tail” for a second lieutenant.
When I went through officer’s training our instructor called us “You fing a**e sucking ladies” a great deal (it was an all male group). I’m not sure if that’s what you want though.
Within the Army there are nicknames for various MOS’s (job’s).
Infantry= Grunt,Ground Pounder, Leg
Tanker = CDAT (computerized dumb ass tanker)
Artillery = Gun Bunny
Medic = Band Aid
Communications = Wire Dog or Radio Dog
Cook = Spoon
Military Police = Momma’s Pussies
Transportation = Clutch
Maintance = Wrench
marine = jar head
A shavetail is a 2nd Lt who was originally an enlisted man but later became an officer, not a 2nd Lt who started out his service as an officer.
IIRC, the term came because the shirts for an enlisted man had more material in the back than an officer’s shirt. If you went from the enlisted ranks to an officer, you would cut (shave) off the extra material to use the same shirt.
Haj
A “mustang” is a person who rose up from the enlisted ranks to become an officer.
Bubblehead for submariner types.
Mushroom for military intel types (work in big buildings with no windows and are fed sh*t).
Sparky or sparkchaser for those who work with electronics.
Well, from some of my Marine frineds with a grim sense of humor
Bullet stoppers, or bullet sponges: Infantry
Speed bumps: Mech Infantry
And from the other side of the fence,
Sky Cops: Air Force
butterbar = Ensign (single gold bar for insignia)
Bull = “senior” ensign in a command
Airedale or “Brown shoe” = aviators
Black shoes or f***ing shoes = surface warfare officers
Hinge = Lieutenant Commander (O4) (the balance point between junior and senior officers)
Boat schooler = Academy grad
plebe = 1st year Academy Midshipman
Continuing the service academy theme, each US academy has its own pet names for the others, just as the services themselves do.
US Air Force Academy: Zoomies/Zoombags
West Point (Army): Time has dimmed my memory of just how we insulted them, but I do remember we had our own motto for them: “Over 200 years of tradition unhampered by progress.”
Annapolis (Navy): Squids, Middies
I also wanted to take a crack at the OP question of whether these terms are considered derogatory. Certainly, on some level they all are, at least, diminutives. However, in 20 years, I’d say that the majority of the time they were used as gentle, almost affectionate, put-downs. After all, the military is historically male-dominated, and you know what a difficult time we males have showing affection for other males. 
Just as every group does, however, the US military has its less broad-minded members (puns intended). Some people just seemed to forget that we were on the same team, and focused more on the differences than the similarities.
I was once chosen as a peacekeeper for the United Nations mission to Western Sahara. I was really excited, because only 2 people from each service waere selected, and being in Space Command, I had never really gotten in touch with my “grunt” side very much. So the 8 of us are in training for this mission to try to bring peace and order to a region torn by hate and intolerance, and the 2 marines have the attitude that they’re the only “real soldiers” there. They barely tolerate the Army guys, and the Air Force and Navy reps are beneath their contempt. Now we all kidded each other, but these two were serious.
Initially, we all just got out our economy-sized salt shakers for these two, but it began to wear. It was a drag, too, because the other 5 guys were really cool, and we were going to be hanging out as a relative minority when we got to Africa (many nations participated in that mission). Their scorn struck home with me especially: as a satellite-driver, I wasn’t exactly Rambo. But one day, I got a little bit tired of being called a pussy just for being Air Force. Striving to know where these guys were coming from, I asked what their regular marine jobs were. They hesitated a second, then told me they were both Judge Advocate Corps. Now lawyer jokes aside, I think that’s that’s just as noble a profession as any other, but I figured these goons had one coming. With as much scorn as I could muster, I replied, “Lawyers? You guys are scum-sucking ambulance chasers, and you call us pussies?” Equally tired of their crap, the others joined in the general derision, and that was the last of their little attitude problem during the training.
I was offered a command between the training and the mission, so I never actually deployed to Western Sahara. I would have liked to see if they did any more growing up when they got there.