According to Wikipedia: 48 states call them counties; Louisiana has parishes, and Alaska has boroughs. And apparently there are some independent cities which are not part of a county but which the census, along with parishes and boroughs call county-equivalent. Fine.
Do you know which one you live in?
This question brought to you by almost 20 years of working in public libraries and constantly being amazed at adults who have no idea what county they live in.
Norfolk County MA.
Maricopa County, Arizona.
To be clear, I’m not actually expecting anyone to say what county. 
I’ll take your word for it.
I’m out on the fringes but I live in Monroe County, NY.
And, like the OP said, one of the reasons I know this is because I know what library system I’m in.
I’d be sorta amazed by that myself, assuming you were an adult with any sort of permanent address ( the homeless without much referent or minors I suppose could take a pass ).
But yes, I do know what county I live in.
Me too. In fairness, I feel like Arizona gets to cheat a little–we only have 15 counties covering the entire state vs. somewhere like Ohio with 80+.
Multnomah County, Oregon
One of my hobbies is taking pictures of county courthouses, so not only do I know what county I live in, but when I travel around within the U.S. I almost always know which county or county-equivalent I am visiting. That’s even when I visited Puerto Rico a few days ago: I knew that in Puerto Rico the municipios are the county-equivalents, and I spent all my time there in San Juan , which is a municipio.
Apache County, Arizona.
We’ve had to get permits. If you want to do everything legally (and get insurance to cover it!), you need a permit, and that comes from the county!
~VOW
Ive always known what county I’ve lived in. Cambria County, PA; Jefferson County, CO; and Pima County, AZ. Is there anybody in the US who doesn’t know?
This is a joke, right?
How the hell could someone NOT know their county?!?!
I live in the largest county (by area) in the US.
I live in the second largest county (by population) in the US. 
I’m gobsmacked that someone wouldn’t know what county or equivalent they live in. Really?
Genesee county.
However, I have a street address/zip code that is one city, but all services (trash, water, fire, police, etc) are provided by a different city and my property taxes get paid to that city. So, which one do I actually live in? That concept has always confused me. Perhaps in some areas there’s a similar blurring when it comes to counties.
Yes, but I also keep a map of what counties in the US I’ve been to, and do things like make maps of local government boundaries for Wikipedia, so I’m probably unusually interested.
Someone who doesn’t deal with the local government much might not have any reason other than curiosity to know. And a lot of people are really incurious.
I’ve never known anyone who didn’t know what county they were in (mainly because I’ve never asked), but I have known intelligent people who had no idea (or were incorrect about) what municipality and/or township they lived in. (But that’s also hard to ask. It’s not always easy to communicate that you want the local government unit, not the mailing address, the school district, the city name tacked on to the front of the name of the subdivision, or what the neighborhood considers itself a part of. Voracious annexation has made the boundaries in the Columbus area really convoluted, so it’s really not that surprising, either. County boundaries are more straightforward, but I can still see people not really caring all that much.)
Um, yes. Montgomery County, MD. I learned this from a very early age listening to the radio on snowy days to see if school was closed. It’s important for a lot of stuff. How could someone not know this?
What is the significance of your county? What services does it provide that would make you aware of its existence? Are there county elections? Do you quote the county name in your address?
I’m making assumptions about what a county does here, but perhaps if you were a renter (so paid no rates/property taxes), never bothered voting, never used local services such as the library etc, then you might not know, or care, what county you lived in.
Yep. I also know that Georgia has 159 counties, second only to Texas in number. That’s pretty much the only fact I remember from my elementary school state history class. Can’t name them all though.
I often have to put it in on forms which ask for my address. And yes, there are county elections, though I’ve never voted in one (I think they’re rolled in with other state elections, but I’m not sure.)
ETA: And if you want to get married, it’s often the County Clerk’s office where you have to go to get the marriage license. Ditto for birth certificate duplicates.