In 1994 I was diagnosed with celiac disease, which led me to create Celiac.com in 1995. I created this site for a single purpose: To help as many people as possible with celiac disease get diagnosed so they can begin to live happy, healthy gluten-free lives. Celiac.com was the first site on the Internet dedicated solely to celiac disease. In 1998 I created The Gluten-Free Mall, Your Special Diet Superstore!, and I am the co-author of the book Cereal Killers, and founder and publisher of Journal of Gluten Sensitivity.
White vinegar or just plain vinegar are typically distilled, and, if so, are gluten-free. Distilled vinegar can be distilled from wheat, corn, potatoes, beets, wood, apples and many other things. Most in the USA are not made from wheat, but are instead made from corn, potatoes or wood, which are all safe (Heinz white vinegar is distilled from corn). Distilled vinegars that are made from wheat are probably gluten-free because of the distillation process described in Frederik Willem Janssens article on this site.
Distilled vinegar made from wood are gluten-free. Wood-based vinegar is often the vinegar used in processed foods.
Flavored vinegars are made with white, distilled vinegar, and flavorings are then added. Some of these may also not be gluten-free (the cheapest vinegars are used since the flavors are masked by the herbs and flavoring).
Malted vinegars are usually not gluten-free.
Red and white wine and balsamic vinegars are gluten-free.