If you are avoiding wheat due to real or perceived intolerance to gluten, you may give sourdough bread a try. It is not recommended if you have been diagnosed with celiac disease, since it still contains gluten.
Avoid commercial sourdough since most will not be authentic. Try local bakeries and ask for a list of ingredients. Or you can make your own (with some patience and time) from a recipe found HERE.
For more information on sourdough click HERE.