Just about all cake-baking recipes, as well as those for quick breads and muffins, call for the pan to be prepped in such a way as to prevent your finished product from sticking to the inside of the pan. Nonstick cookware is supposed to do this on its own, but it’s not foolproof. Recipes recommend that you either grease your pans with butter or cooking spray/oil, or grease your pans and give them a coating of flour.
Between the two choices – greasing and flouring vs. greasing alone – there isn’t always going to be a huge difference in ability of your cake to come out of the pan, but there is a difference between the two techniques. When you grease and flour, the extra layer of flour is going to adhere to the outside of your cake/bread/etc. and give you a kind of “crust” all over. This isn’t particularly desirable for most of these types of baked goods. Cake with a hard side crust? Thanks, but no thanks. That said, the “crust” easily softens up when a cake is cooled and stored in an airtight container of some kind and it doesn’t effect the flavor of the product, so it doesn’t hurt anything to have it.
There are some types of cakes where you really need a crust to form. These cakes are those that are very high in sugar. While it cooks, the sugar caramelizes – especially the sugar nearest to the hot cake pan – and sticks to the metal bakeware. As the cake cools, so does that liquid sugar, crystallizing and sticking firmly to the pan, making it very tough to pry the cake out easily and in one unblemished piece. A good example of this kind of cake is my Carrot Bundt Cake. It needs the help of that flour coating to ensure that it comes out of the pan as easily as possible. You can’t exactly line a bundt pan with parchment paper to prevent sticking, so there isn’t any better way to work it.
Long story short? Greasing alone is usually plenty to prevent your cake/quick bread/etc. from sticking in a cake pan and it certainly gives an edge to even nonstick pans. Greasing and flouring is primarily necessary when you want to have an extra barrier between a high-sugar cake and a pan to decrease the odds of the cake from sticking. If in doubt, I would do both, but most of the time greasing with oil or cooking spray (my two favorites) will be plenty.