Remember the advert "I'm feeling a bit bloated". "Here, have some Bifidus Digestivum!"? I wonder what percentage of the population suffers from bloating, gas pains, constipation, IBS or some degree of failure to absorb the nutrients from their food?
People with Coeliac Disease (CD) or Dermatitis Herpetiformis (DH) (intensely itchy spots on pressure points) have to avoid gluten as much as possible, as it produces an auto-immune response with antibodies that attack their own bodies. However, gluten is also implicated in other conditions due to molecular mimicry. Sjogren's syndrome (dry eyes & other bits) and cerebellar ataxia (brain damage) are mentioned in a huge article by Loren Cordain Cereal Grains: Humanity’s Double-Edged Sword.
This article suggests that there are conditions other than CD & DH which can be helped by switching from gluten-containing grains (wheat, rye, oats, barley & spelt) to non gluten-containing ones (rice, corn, quinoa, buckwheat, millet & amaranth). Luckily, supermarkets like Tesco, Waitrose and Sainsbury's now have a large "Free from" section, which makes finding gluten-free substitutes for breads, cakes, biscuits & breakfast cereals etc a lot easier.
EDIT: See also Keep 'em tight.