We never said it - obviously if the car was still moving we weren’t there yet! But when my little brother was really little, just old enough to tell time, he’d occasionally ask “approximately how much longer will we be driving?” and yes, he actually said approximately 
I was enough older to think it was cute, and our folks would tell him. He’d only ask once per trip, satisfied that it’d only be about X many minutes longer.
Which is certainly more accurate, because if we’re still on the highway in a moving car than of course we’re not there yet.
I can’t recall ever saying it, except in jest. I was the family navigator starting very young, so I was the one directing the driver, as my parents found maps incomprehensible yet I loved them.
They might have asked me but I wouldn’t tell them.
When I was a kid, we only did one big car trip per year, down to the Maine or New Hampshire coast. It was a big deal, my mom acted as “navigator” and would unfold and re-fold the map to show us where we were and where we’d be stopping for lunch.
We did find the trip long and boring, but I don’t think the dreaded phrase was uttered very often.
I’m just wondering - none of your parents said “Well, we’re leaving at 2pm so we’ll probably be there around 5pm” or “oh, maybe we’ll be there at 6” if the kid asked in the middle of a trip? Did none of them figure out about how much time it would take beforehand? Or did an exact time not grok with the kids? Maybe it made it worse for the kids to know the trip would be over 5 hours so your parents wouldn’t say?
I remember being 3 and crying that mom had left for work. Dad told me “She’ll be home at 4:30” and after about 2 days of that routine I figured out that 4:30 meant 4:30 and I just had to wait until that’s what the clock said. It took me another week to figure out that it may be anywhere between 4:25 to 4:50 depending. So for a little while I was upset that she wasn’t there on the dot but figured out estimates fast enough. After that I only needed my parents to tell me our approximate arrival time and I could stick it out. I might have moaned anyway, but that was if I messed up and got myself carsick.
A great idea in theory…however, I think most of us, and certainly all parents, know that time moves slowly for kids. Just think of the week before Christmas…geez, as a kid I thought it was NEVER going to be Christmas - it took forever!
Now it seems like they start selling Christmas crap starting on Labor Day, and it is over before you have time to even finish decorating the house.
So - for car trips - especially if the kids are exited to get there - every minute seems like two hours to a little kid - thus the “are we there yet?!” questions over and over and over.
Or casual clues might be misleading for a kid. When I was young and we’d drive from the suburbs into Chicago to visit grandparents, once I saw city buildings I assumed we must be seconds away from our destination. Why it might take another 25 minutes was beyond me. Or if you’re visiting the Milwaukee zoo and you’ve seen the “Welcome to Wisconsin” sign so why aren’t you looking at elephants yet?
There are signs in Memphis hanging from lamp posts advertising the zoo.
My step daughter and I vastly annoyed Mrs. Plant (v.2.0) by announcing “ZOO!” whenever we saw a sign on our way there. 
Did I say it as a kid? No.
As an adult? Last time some friends and I went on a 900 km road trip, the first time I said it was as we paused to shift from reverse into first after pulling out of the driveway. The last time was when I texted it to the driver a couple of days after we got back.
My local Hobby Lobby had many aisles full of new Christmas stuff set up last week. 
I didn’t say it either, because my father didn’t put up with that kind of thing. He was in charge and you sat quietly until we got there. I don’t remember us ever stopping on the way to Grandma’s (about four hours away).
Kids do say it, and I actually sympathize with them (as well as the parents).
As an adult, I can prepare myself for being stuck in a vehicle for X hours. I can focus on other things than the destination. But even so, in the final hour I might start to think of the destination and get a little impatient.
If I started a journey with no real concept of how long it was going to take, and was just thinking of the destination the entire time, then a long trip would virtually be torture.
This is what my dad did. “Five more minutes” is always the answer. Whenever I go on a long car trip, I ask once, ceremonially, as we’re pulling out of the driveway.
“Are we there yet?” isn’t a real question any more than “How are you?” is. It’s just shorthand for “I’m bored/tired/ready to be done with driving” (and, I guess, longhand for “Hello”, respectively).
As a kid we would have gotten told to shut up if we said it. I don’t remember ever saying it but probably did when I was really young. Neither of my parents would have tolerated that kind of whining. We regularly went on 4+ hour drives to see relatives, too.
As a future parent, I believe I will respond sarcastically too, as it’s kind of my nature. I’m particularly fond of “yup, how’d you know? Go ahead and get out of the car any time (while barreling down the freeway).”
When I was a kid in the 70’s, we lived in Atlanta and had grandparents who lived in North Carolina. We’d make the trip a couple times per year.
It was a 6 hour drive and all we drove on was I-85 the whole way. REALLY hard to judge distances that way. It was said a LOT!
Bob and Tom have a song called Are We There Yet? I think Tom’s children sing on it. Quite humorous.
One of my early road trip memories is asking “Are we there yet?” and finding out we hadn’t even left the county. I was probably only five or six years old, but yeah, I had no perception of time or distance at that point. We had probably been out of our driveway for about twenty minutes. I tried not to ask more but I’m sure I did more than I remember.
Eventually I’d take books, or the Game Boy when I got one, on car trips. I don’t remember ever asking after that.
edit: I’d like to add in defense of irritating children that sitting in a back seat when you’re like two feet tall (or however big kids are) is one of the most boring things in the world. You see the sky out the window and the back of the seat in front of you. It’s not like looking through the front windshield where you get to see things from off in the distance for a long time before you pass them, they just fly past the passenger window.
When my brother Mike was three years old, my dad drove the family from our home in suburban Cleveland to my mom’s parents’ apartment in Manhattan. As we passed the barber shop where we regularly got our hair cut, about a mile from our house, Mike asked “Are we in New Nork* yet?”
- Not a typo, but his actual pronunciation.
Well at least we didn’t have to wear seat belts, or be strapped down like today’s kids.
Plus if you’re prone to carsickness, every moment of suppressing the urge to vomit is interminable. I think that’s one thing I hold against my parents; they rarely medicated us but some motion sickness meds would have made such a huge difference.