Many people have begun avoiding gluten in recent years, some because of Celiac disease, others for other health and dietary reasons. If you are avoiding gluten, should you worry about wine? Generally, the answer is no, but here are some points to keep in mind:
1) The basic ingredients of wine do not contain gluten.
2) If you drink sweet, artificially-flavored wine products, anything might be in those flavorings, including gluten. Also, yuck! Let me encourage you to try a good-quality Riesling or Moscato d'Asti!
3) A tiny amount of gluten can make its way into a wine if it is used as a fining or clarifying agent (this is not very common), or if a wheat paste is used to seal the wine barrels (wax is more commonly used today). In these cases, testing has revealed that the resulting amount of gluten in the wine is less than 10 parts per million. (The FDA's standard for products labelled "gluten free" is that they contain less than 20 parts per million of gluten.) If you are concerned about the barrel issue, you could avoid wines that have spent time in barrels, and stick to wines that will usually not be oaked, such as Pinot Grigio/Gris, Riesling, Sauvignon Blanc, and unoaked Chardonnays.