In Britain: heart, kidney, which I mentioned in the supermarkets thread, and which we ate regularly in the 1940s and 1950s. I eat liver occasionally, kidney in steak and kidney pies, and I recently bought heart for the sake of nostalgia (or something!)
Rabbit was a regular item when I was a child. I've eaten it occasionally since then.
My dad used to eat tripe, which my mum bought specially for him. The rest of us didn't eat it.
Brains; and fish roes. "Soft roes" are like brains, soft and squidgy. "Hard roes" are slightly better, but I still avoid them.
From time to time we had skate. The wings of a ray-like fish, I believe. Very little flesh on them. We regularly had herring, and occasionally bloaters, which I think are herring that have had something done to them, not to my taste.
Brawn. The flesh from a pig's head, boiled for hours and then allowed to cool.
Kangaroo steaks and ostrich steaks. Both available from specialist outlets.
I've had pigeon in restaurants. Tastes quite good, though a but fiddly because it's small, and they warn you to look out for lead shot.
In a market in Leeds I've seen shark for sale, but it wasn't convenient to buy it.
I've had jellied eel in east London, and fresher eel elsewhere; also cooked eel bought in a market in France.
Also, as the thread has "old-fashioned" in the title: mock turtle soup. We had this regularly. I think Heinz mock turtle soup was still available in the 1960s. The only tinned mock turtle soup you can get now comes from Cincinnati, and they put too much tomato into it for the genuine mock turtle taste.
in Zambia: spit-roasted goat. In a hotel in Lusaka at which I was staying in 1970 the dinner menu included "vegetables in season", which turned out to be baked beans.
There were opportunities to try roasted flying termites and some other large insects, but I decided not to. I ate some unknown river fish there too.
In France and Belgium: snails cooked in mushroom sauce and they tasted like mushrooms, though the texture was firmer. Also steak tartare, which is raw minced steak, ordered in error, an interesting experience but I won't repeat it. Horsemeat, several times, enjoyable.
In Malta: various unknown fish. Horsemeat, kangaroo, Rabbit is popular there. I once saw rabbit vindaloo on an Indian restaurant menu.
I would like to try: crocodile; large snake - boa constrictor is said to taste like chicken. I'd also like to try lamphreys, once very popular, and real turtle soup. The local pond when I was about 8 had fresh water mussels, which looked like oysters, but we never tried cooking them.