Why is my apple pie not crispy?
Gluten is what makes doughs chewy, and gluten is associated with high protein flour, so you should try and get low protein ("soft") flour.  Also, the colder your fat (i.e., butter) the flakier and crispier your crust will be.  You also may want to substitute some of the butter for lard or shortening; the lack of water in the lard will also help the crust become crispy and avoid gluten formation associated with hydration of the flour.  Note that you cannot substitute lard/shortening for butter in an equal ratio; you should try and find a recipe that specifically calls for it to get the ratio correct.  As rumtscho noted, you can also blind bake the crust to start its cooking process (but as ElendilTheTall warns, you may not be able to call it a "pie" after that!).  Finally, it may be the case that your pie filling is too moist and therefore makes the interior of the crust very soggy.  I've found that almost all good apple pie recipes call for pre-cooking the apples to remove a lot of their moisture before putting them in the crust.