Just about the only thing better than a ripe, fresh, juicy apple is that same apple and a few of its friends baked into a pie. Of course, much of that fresh juice will cook out of the apples as your pie bakes and will need to be thickened to prevent the pie from boiling over or developing a soggy crust. Cornstarch works well for that purpose, but if you're avoiding corn -- or have simply run out -- there are alternatives.
Plain Old Flour
If your favorite pie-baking apples are dense, long-cooking varieties, ordinary wheat flour is the simplest substitution for the cornstarch in your pie. Flour isn't a purified starch, like cornstarch, so it doesn't have quite the same thickening ability. As a rule, allow 2 tablespoons of flour for every tablespoon of cornstarch you'd ordinarily add. If you're using sugar or a crystalline nonsugar sweetener, mix the flour with it and then toss the apples. If you're using a liquid such as agave nectar, toss the flour with the apples first and then drizzle them with your sweetener.
The problem with ordinary wheat flour is that it takes a long time to reach its full thickening power, and in the interim the juices from your apples will boil merrily. A quicker-acting alternative is instant-mixing or "gravy" flour. This type of flour is precooked at the mill, so -- like cornstarch -- it begins thickening almost immediately, as soon as the hot juices are released from your apples. That means you don't have to choose long-cooking apples, because, unlike regular flour, you won't risk an uncooked, starchy taste in the finished pie.
A few other starches can be used in place of flour or cornstarch, though their availability varies. Instant tapioca thickens pies well, though it leaves its characteristically gelatinous balls throughout your apples. Alternatively, you can grind it in a spice grinder to make tapioca powder, which doesn't form balls but can be a bit stringy. Arrowroot powder makes a fine thickener, very similar to cornstarch in its use. Purified rice starch -- not rice flour -- is the finest-grained of all starches and makes a silky-smooth pie, but it can be difficult to locate if you're in an area without Asian markets.
The Cooked-Filling Alternative
One additional alternative, more common with berries than with apples, is simply to precook your filling. This can be handy for long-cooking apples, or extra-juicy apple varieties. Gently simmer the apples in a saucepan and then drain them, setting them aside. You can thicken their juices with no starch at all by just simmering them until they reduce, thickening slightly due to natural pectin. Recombine the apples and juice in your shell, then bake the pie immediately or freeze it for later baking. This technique can also be used when thickening with flour, to counter the risk of a starchy-tasting filling.