A lot of thickening done in recipes is with wheat flour. Gluten – when wet – is a great thickening agent. However there are PLENTY of ways to thicken sauces, gravies, curries, soups, and chile without using any wheat products.
Canned beans are a great way to make a sauce creamy and thick. I prefer to use chickpeas (garbanzos), or white navy beans to preserve the color of a sauce, but you could really use any beans you like. If you are concerned about sodium, drain and rinse the beans before you puree them in a blender, and add water or coconut milk as needed. Also a great way to sneak some fiber into a meal!
Squash or Pumpkin Puree
Squash or pumpkin puree make great thickeners in curry or creamy soups.
Rice flour makes a great mild-tasting thickener for a roux, gravy, or chile, and it is one of the more common or easy to find gluten free flours. I use Bob’s Red Mill brown rice flour.
Corn starch, Potato starch, Tapioca starch
Cornstarch is very commonplace, and you can actually use all three of the above interchangeably. Corn starch can also be used in chile or gravy.