Here are a few I've heard over the years:
(when I was an NCO):
"Don't you guys carry those sticks so you can beat the soldiers if they screw up?" - I got knuckles (and a few other body parts) rapped more than once in the '50s and '60s
(Later, when I was across the fence):
"You're an officer? Doesn't that mean the troops shine your shoes and press your uniforms?" - they used to, I, like all officers in field units, had a batman/driver who, amongst other things, attended to my kit and quarters in garrison
From a cab driver:
"Do you get a free house and cheap car? Can you walk to the head of the line in the bank? In my old country officers get all that." - well R&Q were 'free' in that they were an untaxed benefit
From several ignorant civvies at various times and places:
"Do you guys have to obey the same law as us?" - yes, but we also have those neat 'laws' in the NDA which don't apply to civvies
"Do you guys pay taxes?" - we (single soldiers and even many married soldiers) did not until E.J. Benson changed things in about 1970
"Isn't your food (house, etc) free?" - see 'free house,' above
"Do you get to take your guns home?" - my rifle sat in an unlocked rack in my room in the quarters (home) in the '60s
"Are you allowed to live off base?" - until about 1965 we weren't unless we were 'lawfully' married (age 21+ for soldiers, age 25+ for officers)
"Do you guys ever talk normal or just scream at each other all the time?" - Eh!?! Don't you have an H4, too?
Cheers