I hear all too often people that state, "white sugar is not vegan". That is technically untrue. While it can be non-vegan because some companies use a bone char filter, that is not the case with every single one. For example, here in Canada we have a company called Rogers sugar. Rogers has several plants that produce their sugar products. Some use bone char, while others do not. The only way to know is by identifying where your town or city gets their supply. In the Yukon we got it from a plant that does use bone char. In Atlantic Canada we get it from a branch of their company called Lantic, this branch is thankfully vegan, with no bone char filtering. On the Rogers website, they actually supply the code to look for to know which plant it is from, which makes it much easier for the vegan consumer.
So what exactly is bone char? Bone char is a granular matter produced by charring animal bones, normally from cattle. It is used as a decolorizing agent for filtering sugar, so it literally means it's making the sugar white.
The only clear cut way to make sure white sugar is vegan is by contacting companies, many also list the information right on their website. The tricky part is when buying processed foods. If it has sugar, it's not easy to know exactly where they got the sugar from. I recommend contacting companies for that as well but I admit, I am far from perfect. It becomes a very tedious task especially when on a budget. So I suggest doing the best you can. This is also why I don't recommend following the "accidentally vegan" lists. Many of these companies, such as Oreos, use bone char sugar. Again, this is totally up to what you feel comfortable with. I presume that the majority of large corporations don't use bone char free sugars, that's why I avoid them when I can.
Here's some sugars that are always vegan:
Coconut palm sugar
Evaporated cane juice
Check out The Vegan Peach to see vegan-friendly sugar and sweets.