Typically, gummy candies contain gelatin to give them a chewy texture, so many chewy candies like sour gummies aren't vegan-friendly. Vegan-friendly gummy candies use vegan gelatin alternatives like pectin and agar agar to give vegan gummies that typical texture without animal by-products.
Candies like chocolate and caramel don't usually contain gelatin, though they can contain non-vegan ingredients such as milk and butter. For this reason, it's always best to check ingredient labels to make sure products are vegan-friendly.