In almost all the places we've lived in Europe, we've found an "ex-pat" food store that featured British and American foods. In Madrid, there's Taste of America. In Rome, we had Sell International - although we more often went to a nearby Castroni. In Vienna, we'd go by Booby's Food Store. Here in The Hague (and nearby Wassenaar), we have Kelly's Expat Shopping. We never did find a good option in Copenhagen.
We don't go by these stores often as prices are brutal. Yet, when you have a specific need...they do come in handy. For example, for Thanksgiving, these places are great to find products (like the above-mentioned pumpkin pie or stovetop stuffing) that are not sold at the local grocery stores. In the USA, the fourth Thursday of November is Thanksgiving Day. Here, it's just... Thursday!
And where else can you find grits! We usually travel to the USA at least two times a year for family & business trips. And yes, we have a suitcase for "supplies" (most ARE foodstuffs). Extra Crunchy Peanut Butter is my go-to.
That said, over the years we have seen more US-products in the larger chain stores in Europe. A few have USA sections that compete directly with the ex-pat food stores. More often than not, there are US-labeled products - like Heinz Ketchup - with slightly different ingredients sold at more reasonable prices (Some "additives" in US foods cannot be sold in the EU). When buying local products, you adjust to a new taste. Here in NL, I've become a huge fan of garlic-truffle-mayonnaise with my FF. This was not part of my palate a few years ago!
In the last twenty years, there has been a huge increase in fast food locations in Europe. Within 750 meters of our Den Haag apartment, we have four McDonalds, two Subways, a Burger King, Dunkin' Donuts, Five Guys, three Starbucks, Dominos, and a KFC. But they're not really a part of our dining experiences (Well, Five Guys is relatively new here, so we have been a few times!). That said, all are packed with locals and very successful.