Grocery Store
So if I was first (Was Apple first even? Surely Nokia had some crappy pre-ovi app store) in having a store selling groceries then I could trademark that and stop any one else having a 'Grocery Store'?
An app is not a term invented by Apple it was used well before cell phones could run 'apps' and a store is pretty well known as a place that sells items. So it seems very generic to me to call your place for selling applications an App Store.... Apple did it better than anyone else and were the first to really integrate it into the phone but that does not mean that they can trademark the name IMO.