I know wheat is the common problem when avoiding gluten, but what about other grains, like barley, rye, or oats?
Note that wheat is a type of grass, and is technically a grain.
Grains without gluten
Not all grains have gluten—only those closely related to wheat do. Grains which do not have gluten include:
Sometimes confused for grains
Note that the following gluten free seeds are not grains, although sometimes they are confused for grains:
Non-grains used as gluten-free starches and flours
Therefore, all grain-like, starchy, or flour-type foods which are not grasses are always gluten free, including wild rice, quinoa (despite any other issues), and so on.
Additionally, flours or seeds based on non-grain seeds, nuts, and legumes are always gluten free, although there may be other dietary sensitivities. These include:
Finally, starches and flours based on roots, rhizomes, and so on are gluten free, including:
Grains containing gluten
The following grains are all wheat relatives, and have gluten to a greater or lesser degree:
Note that the following are all processed wheat products or specific wheat varieties, and should be avoided to maintain gluten free diets:
SAJ14SAJ has great info. But in addition, if you are extremely sensitive to gluten as such with a severe allergy or certain digestive issues cross contamination is frequently an issue. Certain companies are more "allergy friendly" and have separate processing plants. Bob's Red Mill comes to mind for some of their products, but I've seen it with a few other companies as well. It has usually said something about it on the package, boasting about the separate processing plant.
It's usually trace amounts, but I have read quite a few posts from people with Celiac that have issues with the rice flour I pick up for cheap from most Asian specialty stores. So if you're just trying to avoid gluten as a general rule(as opposed to avoiding it because of allergy/illness) this will probably not matter much.