Have you ever begun a recipe, gotten involved in the steps, and suddenly realized that you don't have one of the ingredients? Sometimes this happens, and one of the "ingredients" isn't an ingredient, it's a tool you need. In this case, that tool is parchment paper. Even though parchment is useful, there are ways you can get by without it.
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Alternatives When Baking
When baking a cake, you can use wax paper instead of parchment to line the bottom of your pan. This is because the paper is completely covered by batter and will not be exposed to direct heat.
When baking cookies, you cannot use wax or freezer paper as a substitute for parchment. Those will burn and make a mess of your food and your oven. You can spray your cookie sheet with cooking spray to prevent sticking.
As a more permanent alternative to parchment paper for lining a cookie sheet, consider a Silpat silicone mat. This will also keep your cookies from sticking.
Alternatives For Other Applications
If you need to use parchment to blind-bake a pie crust or to steam food in the oven, aluminum foil will work in a pinch. However, you need to make your foil packet double-thick for steaming unless you're using heavy-duty foil. Regular foil will tear too easily and release the steam you need for cooking.