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:
This is a very good resource regarding the basics of a gluten-free diet.
A friend of mine was gluten-free and he ate a lot of quinoa and rice - however quinoa has come under fire recently. There is a lot of information and recipes online, and depending where you live, there's likely a few people you can speak with for recommendations about what to eat and how to eat it if you're thinking of going gluten-free.