If you're looking to avoid any link between animal products and your food, you might want to take a hard look at the sugar you consume. Cane sugar undergoes a refining process that makes it white, and the process often involves the use of bone char, which typically comes from cows' pelvic bones, Mother Nature Network reports. (Granulated carbon or an ion exchange system can also be used as filters, notes Vegetarian Journal, but the "efficient" and "economical" bone char is the most popular filter.) A process of grinding and then heating them creates the carbon that's used to filter the sugar; a commercial filter can contain as much as 70,000 pounds of char. You aren't actually consuming bone char when you eat the sugar—there's contact, but the end result is free of it—but vegans looking to avoid it need not give up the ingredient.
There are a number of animal-free options. If you buy a bag that's certified USDA organic, for instance, bone char won't have been used to make it. Or you can opt for 100% pure beet sugar; its refining process doesn't include char, and the USDA reports that for the last two decades, sugar beets have made up about 55% of domestic sugar production to sugarcane's 45%. Sugar that's labeled "raw" or "unrefined" is also a good bet, as is sugar made with "evaporated cane juice," MNN notes. Product lists like this one from Ordinary Vegan and this one from PETA can offer some help, too. Things get more complicated when you buy foods that already have sugar in them, since makers might mix different kinds of sugar. (You might want to just try cutting down on sugar, period.)