There is currently some disagreement within the scientific community as to whether oats are independently capable of triggering celiac disease or gluten sensitivity. The prevailing view is that oats are not a trigger, which is reflected in the fact that the Food and Drug Administration's (FDA) Final Rule on Gluten-Free Labeling of Foods contains a definition of "gluten" that does not include oats. However, some research has concluded that the protein avenin, which is primarily found in oats, is capable of triggering celiac disease directly in much the same way gliadin, glutenin, hordein and secalin have been shown to do so.
It is also possible that in some instances where oats might seem to trigger symptoms the actual cause may be cross-contamination with wheat, barley or rye proteins. This can occur at any time between harvesting and when the oats are eaten, including during commercial processing operations or preparation at a restaurant or in your own home. It has also been suggested that some people may have an independent allergy to oats that may cause them to mistake their symptoms for celiac disease or gluten sensitivity. The relative uncertainty surrounding oats and the protein avenin highlight the importance of paying close attention to product labels and your specific symptoms in relation to your diet, diligence in your efforts to avoid cross-contamination, and independent consultation with your doctor.
About the debate over whether oats trigger celiac disease ... Try starting here and here
About the USDA's classification of oats ... Read the United States Standards for Oats [PDF]
About the different species of oats ... Take a look at the USDA Classification Reports for Avena L. and others in the grass family
About the oats you just might have eaten for breakfast recently ... Take a look at the USDA profile for common oats
About the different types of oats ... Check out the USDA Commodity Image Gallery