Whole grains are nocturnally superior to grains that have been processed in any way. The more the grain has been processed, the more nutrition it looses.
If you process the grain yourself, and then eat it immediately, then you are OK. After all, when you chew something, you are already starting to process it.
For example, if you mill your own flour directly from whole grains, and then bake with it, you will have minimized oxidation; oxidized food degrades food quality.
If you are allergic to wheat, you may find this list of alternative whole grains to be helpful:
Notes:
* There is some debate in the celiac community as to whether oats are or are not safe if you suffer from celiac disease.
** Not suitable for people suffering from celiac disease.
What to do with them? Check out this gluten-free breakfast recipe.