To me, the best tasting sugar is raw cane sugar. This is basically juice squeezed from cane stalks that has been dried into crystals. It has a blond or pale amber color due to the molasses compounds that are still present. This is what makes raw cane special - the flavor depth is marvelous with overtones of vanilla, caramel, and of course molasses.
Backing up a bit, most sugar is made from either cane or beets. Cane is tropical and beets are grown in temperate climates. Cane stalks are squeezed and mixed with water to make juice. Beets are sliced in immersed in water to leach out the sugar. Some impurities are precipitated out with lime and then the evaporation process begins. The juice is heated and water is driven off to make a syrup. The syrup is cooled and crystals form. The crystals and syrup are then spun in a centrifuge. The left over molasses goes one way, the raw sugar crystals go the other. This stage is also called "turbinado" sugar for the turbine-like looks of the centrifuge. Of the commercial varities I have tested, turbinado is a little darker than raw which may come from factory variations or which stage of centrifuge was pulled. Demerara sugar, named after the historic Dutch colony that is now part of Guyana, is quite similar to turbinado.
Anyway, the uncrystallized syrupy part coming out of the centrifuge is the molasses. There are various grades of this also, but the key thing is this: beet molasses is fed to pigs, cane molasses makes great cookies! Although they are both mainly sucrose, cane rules. High class chefs will only use cane because of the way the small remaining impurities act during critical baking like souffles.
For ordinary table sugar, the raw sugar is re-melted and highly purified to remove color and flavor. In a taste comparison, it is just plain dull. A final (weak) bit of evidence suporting raw sugar is that raw sugar retains some minerals that are actually nutritional. Some folks try to make a big deal of this, but, um, it is still 99% sugar.
White sugar is so dominant these days that most brown sugar is now made from white sugar by adding molasses back in (which is a little daft). Back in the day, various forms of brown sugar were made from raw cane juice that may or may not be clarified with lime. Muscovado is a darker brown sugar made by evaporating the juice without spinning in a 'fuge.
Well, you made it. You are now officially a sugar geek.