I think I’m an outlier, but I pretty much always eat them. For me, it gives a satisfying crunch, like meaty potato chips. Especially if they’re seasoned. But I Am NOT A Foodie, so I definitely wouldn’t say when you’re “supposed” to eat them.
When I was 21, old enough to get into trouble but still very young and naive, I was at a bar that served complimentary “peel and eat” shrimp for Happy Hour. Except I missed, and nobody told me, the “peel and…” part. Crunching on the shrimp, shell and all, trying to chew it thoroughly enough to safely swallow it, I thought “who enjoys this?”
Nowadays the closest I get to eating the shells is when, like @Chefguy, I make stock of them.
Incidentally, I used to listen to Neil DeGrasse Tyson’s StarTalk podast and he mentioned once that he sometimes ate shrimp shell and all, so there ya go.
I believe in Asian countries where the shrimp is fried the shells are meant to be eaten. According to this article, you should eat the shells (as long as they are coated in corn starch and deep-fried):
No thank you. One personal pet peeve is dishes like fancy shrimp pasta you get in a restaurant where they leave the tails on because it looks nice, and I have to get my fingers all saucy pulling them off.
I was in Spain with my (now ex) wife and we ordered peel and eat shrimp. We were delivered a huge plate of shrimp that were steaming hot. You could not touch them to peel them. So, we sat there with the plate in front of us waiting for it to cool down.
We didn’t mind so much because we had drinks but it was a stupid restaurant experience.
Salt-and-pepper shrimp (as shown in the photograph in the article) is the one case where I eat some of the shrimp shell. The coating just tastes so good…
I’m from Maryland and steamed shrimp is right up there with steamed crabs. You steam the shrimp with the shells on to keep them moist, and the Old Bay gets steamed on the shells. If you peel the shrimp first the ratio of Old Bay to shrimp gets thrown off. The perfect amount of Old bay is the amount you get on your fingers while peeling the shrimp. Fresh from the steamer can be a little tricky trying to peel w/out burning your fingers, but one or two into it they are cool enough. I’ve never heard of shrimp cocktail with the peels on - well just the tails, yeah.
Once in Morocco I had a dish with shrimp in it where you were meant to eat the shells. The shells were much thinner than normal and seasoned/fried as mentioned above. The was a lady from Italy on that trip that insisted on peeling them, even after we showed her the shells could be eaten.
We used to go to the fish market in WDC back in 90s before it got so big. The steamed shrimp with Old Bay was wonderful. You’d stand at one of the tables and peel/eat to your heart’s content.