Don't recall alot of these.
Infantry: grunt, ground pounder, dog face or line doggie.
Artillery: cannon cocker, red leg.
Paratrooper: bird sh*t ["Only 2 things falls out of the sky; bird sh*t and fools".]
Non-jump qualified: leg, straight leg, dirty ol' smelly leg, chicken sh*t ["Yeah, the only thing that stays on the ground is chicken sh*t".]
Sailor: swabby, squid, anchor clanker
Airman: propellor smeller, bus driver [because of the dress blue uniform]
Marine: jarhead, gyrene, leatherneck, devil dog, our dim-witted cousins
Special Forces: green beanies
We made more fun of the other guy's division, mostly based on their shoulder patch.
101st Abn. Div.: Screaming Eagles; Pukin' Buzzards; Screamin' Chickens [The Vietnamese didn't have a word for "eagle", so Charlie called us the "Chicken Men"]
82nd Abn. Div.: All American; Alcoholic Airborne; African Airborne; Almost Airborne.
1st Inf. Div.: Big Red One; "You have to be one, to be in the Big Red One" [said with a limp wrist and a lisp]
25th Inf. Div.: Tropic Lightening; Electric Strawberry; Cu Chi National Guard
1st Cav. Div.: Horse Soldiers; Horse Blanket; "The horse that was never rode; the line that was never crossed; and the color is the reason why".
9th Inf. Div.: Psychadelic Cookie.
173rd Abn. Bde.: The Third Herd; "Chicken wing with a butter knife in it".
4th Inf. Div.: Ivy Division; Poison Ivy
1st Logistical Command: The Leaning Sh*thouse.
5th Special Forces: Electric Butterknife
196th Light Inf. Bde.: The Burning Worm
I know there's more that I'm not recalling right now. Add to it, boys.