Having a US Postal address is very helpful. We don't have to pay international shipping costs to buy stuff we want. Amazon Prime is even better - one flat annual fee and lots of stuff comes to us with no additional shipping cost.
From time to time though we come across stuff that does not ship to APO addresses. It is an odd assortment of things, so I thought I would share -
Companies will not ship the following (I should note for accuracy sake - the stuff can be shipped and mom has been great about being our private shipper)
Scrapbooking Supplies (albums, papers, stickers)
Pencils (but we can and did get a pencil sharpener)
Shampoo for people (but yes to shampoo for dogs)
Car Battery (yes to tires)
Bitter Apple Spray that keeps dogs from chewing stuff (like their own paws)
Noise Canceling Headphones
Customized Converse Sneakers (but regular ones yes)
Mitt for Carwashing (but yes to soap to wash the car)
Car Emergency Kit - the ones with that orange triangle
Even with these and other "no" products we are extremely fortunate to be able to order many of the things we use on a regular basis. Between Amazon and our PX American consumer goods are plentiful and it's not like we really need any of it, but it does make life more comfortable and for that we are grateful.