Some vegetarians--usually strict vegans--will not consume sugar. This is because sugar is often whitened with bone char from cows.
If you are a vegetarian and you want to continue eating products that contain sugar, but do not want to cause suffering in the process, you have a number of options.
Your first option is to only consume products made with beet sugar. There are two major sources of sugar in the United States: beet sugar and cane sugar. Cane sugar is often whitened with bone char from cows; in contrast, beet sugar is never whitened with bone char.
So, if you want to completely avoid the bone char, you can do so by eating only beet sugar. The only challenge--and it is a big one--is finding out which foods contain beet sugar and which foods contain cane sugar.
To make things more complex, you can also consume a number of types of cane sugar, as long as you are willing to find out what the source of the sugar is.
You can do this in a lot of cases by looking at the nutritional panel on food before you buy it. If it says fructose or dextrose, the sugar is from a plant source (either beet or corn). If it says sucrose, it could be from a number of sources, which could include bone char-whitened cane sugar.
Now, if you are cooking with sugar, you can personally verify that is bone-char free by purchasing from the following companies, which have publicly-stated that they do not use bone-char: Florida Crystals Refinery, Imperial Sugar Company, Irish Sugar Ltd., Sugar In the Raw (which is also less-refined), and American Crystal Sugar Company.
If you can’t find these brands, but want to avoid consuming bone-char sugar if possible, you can avoid these brands, which have publicly-stated that they do use bone-char: Domino, Savannah Foods, and C&H Sugar Company.