There is no gluten in vanilla beans. This does not mean that products advertised as vanilla are gluten-free. The vanilla bean itself, though, does not contain the proteins that can be harmful to those with celiac disease.
One of the most often used forms of vanilla is vanilla extract. The U.S. Food and Drug Administration (FDA) has established stringent guidelines about what can be called pure vanilla extract. These rules say "pure" extract can only contain a small amount of ingredients other than vanilla, and none of those ingredients contains gluten.
Some of the confusion about gluten in vanilla extract comes from the idea that the alcohol used to help pull the flavor from the vanilla beans could be distilled from gluten-containing grains. Even if it were, the alcohol used in pure vanilla extract must be distilled as dictated by FDA guidelines. The distillation process involves turning liquids into a gas and then cooling the gas back into a liquid again. The proteins that are dangerous to those with celiac disease are not able to be changed into a gaseous form and are removed from the alcohol through the distillation process. This means that whatever type of distilled alcohol is used in pure vanilla extract, it will not contain glutens.
Another product that contains vanilla is ice cream. There is no gluten in vanilla ice cream, but there could be other components that can carry gluten into it. Depending on the facility where the ice cream was produced, it is possible that contamination from gluten-containing ingredients used in other products or flavors could make their way into the ice cream. Vanilla ice cream that has added flavorings might not be gluten-free either, especially if the added ingredients are from a separate manufacturer. There are brands of ice cream available, though, that do clearly say they are gluten free.
Gluten in vanilla could be found in the powdered forms used in high-volume kitchens and for industrial production. The process and the ingredients added to achieve the final product might contain the harmful proteins. This can be especially problematic for those with celiac disease, because not all kitchens are aware of the gluten content of the powder, making their dishes potentially dangerous.
For those still in doubt, the best practice might be to purchase vanilla beans whole. With absolutely no potential for finding gluten in vanilla beans, they could be used in gluten-free recipes. There also are ways that a vanilla extract could be made at home using water or neutral distilled alcohols.