I used to peel off the thin wax layer that covers red apples. Is this necessary?
The food-grade wax applied to apples after being washed post-harvesting (which removes their naturally produced waxy outer coating) is safe.
From the U.S. Apple Association:
That said, if the layer of wax is so thick that you can peel it off, it wouldn't hurt to brush it off under warm water; wax isn't digestible. (I use a speck of Dawn or a spritz of enzymatic vegetable/fruit spray to clean my apples because I hate the added wax.)
If you're eating red delicious apples coated in thick wax, you are really missing out on the wonder of dense, sweet, crisp, tart apples. Red delicious have an unnaturally thick skin, mealy flesh, and little apple flavor. I highly, highly recommend some Gala, McIntosh, or other smaller, rounder, really delicious apples.
Also, it's at least a good idea to rinse with a light soap/vegetable wash since the wax can pick up dirt and bacteria.