Most breakfast cereals come in a box that contains a plastic bag. I have mostly stopped buying breakfast cereals, but oatmeal is necessary for one family member. Quaker brand sells a box with no plastic bag, at least they do where I live.
I had been buying Jordans because of the conservation aspect and because they taste better. Jordans has a plastic bag.
If you have the option of buying breakfast cereals in bulk, it is worth considering.
Target sells organic cereal without a plastic liner. Its a box with a plastic flip top lid. Not sure which is worse, but at least its a step in the right direction.