In today’s paper, there’s a recipe for Easy shrimp make an elegant meal. From the link:
How are you (properly) supposed to eat shrimp with sauce on it, and with the tails still on?
I have a similar problem with those clam seafood dishes with the clam still in the shells. I can kind of dig it out, but not very well, and it’s a pain, so I avoid ordering it.
If the tail’s still on the shrimp, stick your fork through the base of the tail, and then put the other end of the shrimp in your mouth.
Suck slightly, rotate and pull. The serrations from your fork into the meat make it rip nice and even, and you get the majority of the meat out of the tail.
If I’m at a truly elegant dinner, and they serve shrimp in sauce with the tails on, I’ve always just cut the tails off and didn’t worry about the meat in them.
My mother always complains to the waitress whenever she orders something like that and it appears with the tails still on. Shrimp and grits tends to be a frequent offender. She sticks her fingers in and pulls them out, because she loves shrimp and doesn’t want to miss any shrimp meat. I’m glad she complains - seriously, who’s supposed to eat that crap neatly?
See, this is why I like salt-and-pepper shrimp. You just eat the whole thing. (I eat the heads first.)
It can be daunting to eat it neatly (the cutting off the tails with your fork seems to be the preferred method etiquette-wise) but tail-on shrimp is important to some dishes and sauces…it provides a wonderful flavor (or depth of flavor) that is unattainable if the shrimp is cooked without the tail (or shells, but who wants shells mucking about in their sauce?).
I cut off the tail if eating in public or amongst those possibly more cultured than I, but if eating at home and the shrimp is in a messy sauce, I will bite off the shrimp (sucking the tail meat as described above) but keep the actual tail out of my mouth and on the fork to be placed at the side of the dish.
How to eat pasta with sauce and seafood with tails still on
I always remove my tails before eating pasta and seafood 
Does anyone just eat the tails?
Or is it just me that does that?
That depends on the shrimp. If they are tiny and the tails won’t be that “chokey” then sometimes I do, but if they are larger and more noticeable, I wouldn’t advise it.
If I’m eating at home, I pick up the tail with my fingers, messy or not. Hey, that’s what fingers are for.
Somebody had to say it…
I’ve been known to do that in public.
What? 
This is someone who prefers to take sushi home to eat, because it’s so messy. I can’t eat the whole thing in one bite, and two bites, well…it makes a mess!
Actually, it’s not that difficult. Spear the shrimp with your fork close to the tail. Put the point of your knife under the shell and push back to the end of the tail. Sever the shrimp meat where it meets the shell. Eat your complete shrimp, wasting nothing, and give your table companions a smug look.
Pasta with sauce is also not a major challenge. Just make sure you haven’t gotten too many strands when you start to twirl, and don’t try to set a speed record – you’re trying to limit the splatter possibilities.
Great. Now I’m hungry for pasta with shrimp.
Yeah, best strategy with eating pasta neatly is to put less on your fork. If you really can’t eat it, the sauce is too thin and doesn’t stick enough.
As for seafood; I may try the above strategies, but I tend to just use my fingers, at least for shrimp. Shells etc I empty using my knife.
I just eat shrimp tails and all. You tail peelers are a bunch of food-sissies.
What about taking the tails off before cooking, but putting them in the pot with the rest, and then fishing them out at the end like bay leaves? It seems like that would give the same flavor, while making the experience easier on the diner.
Won’t eating the tails (or any kind of hard shellfish shell) on a regular basis cause a violent and possibly deadly case of appendicitis?
Here’s what I figger’… the shrimp tail- that’s one of the culinary world’s natural “handles”. Like a rib, a drumstick, or a stem it is beggin to be picked up and grasped, handily and digitally…
I like you.
When I order shrimp at the mexican place, I just use my fingers. If the deputies or the guys from the house painting/ lawn care service at the next table don’t like it. Too bad.
The shrimp with tail and sauce is the Strawberry of the Sea. You hold it upon the stem… the juices to your mouth, staining your fingers. Most don’t eat the strawberry stem, discarding the perfect incisor tooth composite in the circumsized strawberry’s soft red flesh along with the greenery. Ever popped a strawberry? The stem chlorophyl completes the berry experience.