Vinegar
Vinegar is a sour liquid made by fermenting a plant. Mostly sourced from fruit-juice like apple-cider, wine or grains like rice. It is used in cooking and pickling.
Luckily Most vinegar's are considered vegan, unless it was processed with Gelatin or isinglass or other animal products.
If the Vinegar is made from wines and beers that have already been fined by isinglass or gelatin, such vinegar is non-vegan.
Not very common is vinegar that contains honey, which will usually be stated on the label.
Balsamic vinegar
Is produced by fermenting grape juice for a number of years and letting it form naturally.