As an American cook and eater, you can't say enough about apples; they're in our blood.
Which is fortunate, and not coincidental, because apples may be the most versatile fruit there is. You can roast, sauté, bake, stew, or fry them -- or eat them raw, of course -- and they take just as well to savory seasonings as to sweet ones.
This isn't even to mention the fact that there are literally thousands of varieties of apples, each with its own character (though, sadly, we don't see as many of these as we once did). Generally, apple varieties fall into one of three categories: eating (such as Fuji or Gala), cooking (like Rome and Ida Red), or all-purpose (including Granny Smith, Golden Delicious, and McIntosh). It's not that you can't cook an eating apple, or eat a cooking apple raw. But eating apples tend to have a sweet flavor and crisp texture that fade or get masked when you cook them, while cooking apples are often tart and soft raw-qualities that you can appreciate better after cooking and seasoning.
Leaving the skins on apples is almost always an option, but if you prefer your apple pandowdy, applesauce, or whatever else you're making peel-less, use a vegetable peeler to take off strips from the stem end to the flower end (or around the circumference, if you prefer-it really doesn't matter).
Coring apples before cooking is not optional, but there are several ways to do it: If you want to keep the apple intact, dig into either the stem end or the flower end with a melon-ball cutter or a small spoon to remove all the seeds. If you're slicing the apple anyway, cut it into quarters and cut the core out of each wedge with a paring knife. If you cook regularly with apples, invest in a slicer/corer -- you position it above the stem and then push it down; it slices and takes out the core in one fell swoop. Apples begin to brown quickly after you slice them, so if appearance matters to you (and it's a purely aesthetic issue-browned apples still taste fine), squeeze a little lemon or lime juice over the slices.
What to Make With Apples -- Sweet and Savory
And after you've sliced them? Apple pie is the obvious thing to make, but as far as I'm concerned, it's one of the worst ways to use apples -- too much crust, too little flavor. If I'm going to serve apples for dessert, I'd much rather sauté slices in butter until they're nice and tender, add sugar and cinnamon and cook until they caramelize, and serve over ice cream or yogurt. Or, for something a little more refined, I layer apple slices in the bottom of a skillet with butter and brown sugar, top with a simple buttermilk-based cake batter, and bake. Apple Upside-Down Cake looks fancy but is in fact quite simple to throw together -- much easier than pie, and better tasting, too.
But I'm just as likely to cook apples without any added sugar and serve them as a savory side dish alongside meat or vegetables. Try sautéing apples with onions and serving them with pork chops or roast chicken. Or, even better, roast apples with parsnips (sweet potatoes or turnips work, too) and a sprinkling of curry powder for a warmly spiced, ever so slightly sweet autumn side dish.