Plant a seed from your favorite apple and you will eventually grow...something else.
Apples are extremely heterozygous and do not breed true. Instead apple trees are propagated by grafting--by stitching together a cutting of the desired fruit onto a living stump. (Kevin Hauser has this short video detailing one such grafting technique.)
Farmers and nurseries once used any old apple seedling for rootstock, but today they usually choose from rootstocks that cause the tree to bear quickly and/or for size (that is, to grow the grafted variety on dwarf or semidwarf trees).
These rootstocks are similarly propagated asexually from clippings--usually some variation of sticking live rootstock clippings into dirt or other medium until they root.
(Update: Kevin Hauser also documents that process on video.)
Consequently your favorite apple probably grew on a single tree comprising not one but two clones.
Incidentally, "Rootstock" would make a great name for pomological convention.