Depends on the apple.
Apples with softer skins will bake to a more even consistency, but apples with tough skin (the 'shiny' kinds like McIntosh or Red Delicious) tend to get caught in your teeth and throat, and are generally a pain to eat.
If you do make a pie with the skins on, use smaller pieces of apple or slice around the apples to create shorter pieces of peel.
These are easier to eat and don't get caught in your mouth as much.
cooking.stackexchange.com/users/624/Adam Shiemke
When making fruit pies your goal is essentially to make a loose jam inside the crust, something that will remain firm and cohesive without resisting fork or tooth.
Apple skins are detrimental to this process as they aren't hygroscopic and will prevent the apple pieces from melding with the other pieces on the skinned side.
I'm not saying it's impossible to make a nice, firm apple pie with skins on, but it's far more likely for that slice of deliciousness to collapse on your plate than if you peel them beforehand.
cooking.stackexchange.com/users/990/Mike Yockey
You should peel your apples.
If you don't it gets hard and rough and isn't pleasant.
The nutritional value is pretty much lost because it gets cooked.
Just eat the peel you've got left :)
cooking.stackexchange.com/users/568/configurator
Try it with the peel pureed.
I've made a few pies this way
and it works well - also adds a bit of color!
Really thoroughly wash the apples Cut-out any bad-spots Peel 'em!
Throw some of the apple-slices in with the peel and blend.
Use a stick-blender for best results Toss the puree in with the rest of the apple-mix and bake!
cooking.stackexchange.com/users/18159/john3103
In my experience cookbooks always tell you to peel the apples, and professional apple pies will always have the peels removed.
Cooking at home, though, I often leave them on, especially if I know the apples are organic.
I think the peels add flavor and texture, and as you mention, nutrition.
cooking.stackexchange.com/users/288/bess
I leave the skins on, slice the apples, and soak them in cinnamon, sugar, and a little salt for a day or two.
Then I drain and layer the pie with apples, cinnamon, and sugar several times and bake.
I've never had complaints.
The skins basically turn to mush but the pie is great, not a sloppy mess.
Very nice on a plate, holds well while cutting and serving, and saves a lot of time not peeling apples.
That's my .02.
cooking.stackexchange.com/users/6899/big d 
I always leave on the peel I love how it tastes I also don't remove the skin when I eat a fresh apple.
I really don't like any apple pies from the market
so I tend to just bake them myself as they are so easy to make and taste totally different from manufactured pies.
cooking.stackexchange.com/users/26900/Diana
Been haking apple pies from our trees for the last 3 years.
Everyone loves my pies and no one notices that they aren't peeled.
They are surprised when I tell them they had skins on.
cooking.stackexchange.com/users/77308/Linda White
Better Homes and Gardens offers an Unpeeled Apple Pie recipe that looks exactly like a regular apple pie recipe, except that you don't peel the apples.
Guess
their test kitchen found it edible!
I'm about to try unpeeled apple turnovers myself, using my regular recipe.
Here's the BH&G link: http://www.bhg.com/recipe/pies/no-peel-apple-pie/
cooking.stackexchange.com/users/40396/Mary Ellen
Is it okay to leave the skin on the apples when making an apple pie? I'd like to leave them on, but I wonder if there will be chewy strings of peel or if they will cook tender.
Apple pie: peel or not?
cooking.stackexchange.com
<pie><apples>
cooking.stackexchange.com/questions/1551
cooking.stackexchange.com/users/419/John Dyer
Professionals usually say to peel the apples first, but some recipes do use the peel and may be preferred. Apples with softer skins will work better, but you could puree the peel or soak the apple slices in cinnamon, sugar, and a little salt for a day or two to soften them. It is a question of taste and the variety of apple as to whether you need to peel the skins or not.
It depends on the variety of apple and thickness of the skin. There are recipes that don't require you to peel the apples. Most cookbooks tell you to peel the apples. Try soaking the apples in sugar and cinnamon first, with the skins on.