I’m going to just slink back out of this thread without posting any of the (comparatively quite tame) things I ate as a kid. 
Oh, you poor, poor people… 
Not my family, but me as a kid: mustard on bread.
Chicken hearts are good too.
We had fish heads quite a lot. In soups, stews, jook, roasted on their own with rice. The eyes are the best part.
Fried rabbit used to be common and carried by most super markets. Calf brains and eggs, liver at least once a week, now only rarely. Occasionaly duck now never. Canned turtle soup was not uncommon and very good. Lamb and veal were both more common than now as well.
Lots of things in this thread that sound unappetizing, that’s the first one that’s completely off-putting to me.
Scrapple! Luscious, greasy, salty scrapple. I gotta go.
Well, we didn’t have a lot of money and, like chicken hearts, they were dirt cheap (usually they’d toss in the tails for free).
If you don’t want to eat the inner-head stuff, there’s still quite a bit of actual meat on it (you generally get from just behind the fins). The cheeks are particularly good.
Where are you from? I grew up in Maryland, and didn’t realize until I moved away that scrapple is really only a thing within about a 400 mile radius of Washington DC. Not only did people out West not eat it, they hadn’t even heard of it.
The markets here usually have them, and you can find fried chicken gizzards at some of the fried chicken places. Personally, we didn’t grow up with a lot of gizzards–just maybe in the soup or stuffing.
Now chicken livers is another thing. When I was a kid and we’d settle down into an “ABC Sunday Night movie” or something similar, my mom would often bake up a tray of chicken livers wrapped in bacon and held in place by a toothpick, as some sort of quasi-rumaki sort of thing. I loved those things!
Also, especially for a weekend breakfast, kiszka (a type of Polish blood sausage/black pudding) was a common and welcome treat. Still love the stuff.
There’s probably a whole mess of other things we ate that might be considered “weird,” but those are the ones that more immediately come to mind. Oh, and tripe. Polish tripe soup was a family favorite, even by my brother who dislikes a lot of the stereotypical Polish food and is not, in general, a fan of offal.
ETA: Oh, just thought of an obvious one that makes most people wretch at the sight/thought of: Polish style aspics. The most common type in my family is similar to that one: chicken, egg, peas, carrots, suspended in a gelatinized broth. We’d typically eat it served with vinegar poured over it and a slice of hearty bread. I really love this stuff, but I’ve never met anyone who is not Eastern/Central European who will go anywhere near it. It was generally eaten as a snack or light lunch.
Hominy grits, scrapple, rice with condensed milk with sugar and cinnamon as dessert.
Their loss. Scrapple is amazing! I like to cut it relatively thick and fry the shit out of it so the outside is crispy but the center is almost liquid.
It squicks people out because of what they’d heard it’s made from (“everything but the oink”), but if you serve it to someone who doesn’t know what it is, they always like it.
Yeah, I like it too. (Maybe I do belong in this thread, despite my first post…)
I like it sliced thin and pan-fried so that it’s more crust than mush, and the crispy slices made into a sandwich. The Wikipedia article on scrapple actually has a picture of that very application.
We four children would spend an afternoon catching catfish and a couple if buckets of frogs. When we got back my Gran would pan fry them up fresh–yummy!
(I admit part of the allure of the froglegs was getting to drop them into the hot pan and watch them kick and ‘swim’ across the pan!)
I’d trade a year of my life to sit down for such a meal with my Gran, just one more time!
Braunschweiger on buttered toast. But only for breakfast.
Side note: The spell checker wants to change braunschweiger to Schwarzenegger.
That would inspire some people to smear Jell-o on the kitchen floor and set the sofa on fire.
My father worked in a meat-packing plant for several years when I was young (in the office, if that makes any difference) and he brought home lots of cheap cuts of meat. We did have tongue from time to time, but mostly for sandwiches. That’s the only odd one I can remember.
When my mother bought chicken it was always whole birds with the giblets (heart, gizzard, liver and neck, I think) and she would cook those up with the rest of it. I ate the liver, my sister ate the other pieces, even the neck - she liked to pick the bits of meat out with her fingernails and leave a perfectly clean set of neckbones.
We never had bread with our meals, my father wouldn’t have it. I think it reminded him of the poverty of his childhood somehow. We had potatoes or other starches instead.
My mother was a fairly ambitious cook for the time ('50’s and '60’s) and for someone who worked full time as well as doing all the cooking, and made dishes that you wouldn’t have found in very many homes, like Turkey Tetrazzini and Beef Stroganoff. Mostly it was a way to use up leftover meat and to make a casserole in advance that could just be popped into the oven when she came home from work.
OK, I do have one.
Growing up in a mixed household as I did, I ate phở regularly at a time long before there were phở joints all over every major city. Which means I’ve never been a stranger to eating things like tendon and tripe.
Beach plum jelly. Next to impossible to buy these days.
Beef tongue. Haven’t had it in years, but I used to like the part with the taste buds for their mouthfeel.
Steamer clams. There are soft-shell clams. Once steamed, you take some of the broth and melted butter. You pull the skin from the neck (siphon, technically), and holding it by the neck, dip it in the broth (to rinse off sand) and the butter. I’ve seen them from time-to-time as “Ipswitch clams,” but they are usually served fried (which is ok, but they aren’t steamers).
I’ve never had tongue in the old school Continental cuisine, buried in aspic way, but it’s a typical taco cart meat choice, and probably my favorite. Mmm…taco de lengua.
Is scrapple the same thing that we in the South call souse? I’ve seen souse at the store but never tried it. This may be all I need to give it a try. Scrapple sounds yummy.
As for my contribution to the thread, we had my dad’s meatloaf. Before I tell you how it’s made, you need to know that my dad was born in 1920, one of 7 children, in destitute poverty, suffered through the depression (Dad: “What depression? We didn’t have enough to eat or any money before the depression and so it really wasn’t much different for us.”), was put on a orphan train as a young boy with his brother and basically lived in a farm family’s barn working the fields and animals all day until his mother could manage to get them back about a year later, served in the Pacific in WWII, was captured in Bataan and was a POW for 3 1/2 years losing almost 100 pounds from 190 to 95 during that time before they were liberated, so, quite frankly, he was just happy to have ENOUGH food on the table and happy that it was identifiable food on the table. 
So here’s Dad’s meatloaf recipe:
Get out your meatloaf pan and spray the inside with some Pam cooking spray.
Take your 2 lbs of hamburger and make it into a rough loaf shape.
Put it in the pan and stuff it down to make sure it all gets down in there good. Sprinkle with a little salt and pepper on the top.
Put it in the oven and cook it until it’s done. Slice and serve.
Sigh. I adored my Dad and I still miss him even though he’s been gone 30 years. He was a devoted son, a great husband, a terrific father, a good citizen, and a war hero…but he was no cook.
I was an older kid before I tasted “real” meatloaf made a friend’s house and found out just what I had been missing.