Studies are inconclusive, as far as I'm aware.

Anecdotal evidence certainly exists in abundance: people eat gluten and react. People avoid gluten and feel better. However, intolerance is not an allergy like Celiac's; an allergy is defined by an IgE antibody reaction. People who claim to be sensitive to gluten, who are not specifically Celiac sufferers, do not produce IgE in response to gluten.

Additionally, blinded studies, in which patients claiming to be intolerant to gluten were given a variety of breads to eat, could not tell between the gluten-containing and gluten-free breads. This suggests many anecdotal cases are psychosomatic; people associated some other stomach/gut reaction incorrectly with gluten, or have convinced themselves it is gluten without considering getting other things, like fructose tolerance or IBS, tested.