Oats are another grain which store well long term. Almost all edible forms of whole oats, including groats, are dehulled and heat processed to stabilize the oil content.3 Because of this stabilizing process, oat products do not as readily become rancid. A recent study done by BYU1 showed that rolled-oats stored in #10 cans were still considered acceptable for emergency consumption after 30 years. Rolled oats were preferred over quick oats in taste tests of the samples that had been stored long-term. The amount of oxygen present in the storage containers significantly affected the taste quality. So, it is important to make sure that rolled oats are stored with oxygen absorbers in sturdy, quality containers that maintain their seals.
I have seen a recent trend of families storing whole-oat groats (which are the heat-processed and dehulled oat seeds), and purchasing a roller to create their own rolled oats. Certainly, if you love freshly rolled oats and can afford the roller or attachment, which can cost from $75 to $500, this is an acceptable choice. However, given BYU's study showing that rolled oats can be stored well long term, you might choose instead to store carefully packaged rolled oats and apply your savings to other areas of home storage.
Oats are available in several different forms:
Oat Groats - The dehulled and heat/steam stabilized oat seed.
Rolled Oats - Groats that have been rolled. Also called old-fashioned.
Quick Oats - Oats that are rolled more thinly than rolled oats and steamed to reduce cooking time. Do not store as well as rolled oats.1
Steel Cut Oats - Groats that are chopped with a sharp blade into small pieces.
Just as I've mentioned with all of the other grains, it is important that the moisture content of your oats be less than 10% at storage.
1 - BYU Food Storage Research
2 - Selecting & Buying Grains (Alan T. Hagan)
3 - Can-Oat Milling
4 - Wikipedia: Oats (see kilning)