The amount of salt in a stick of butter can vary, which can cause problems in your cooking. Salted butter can contain as much as 3 percent salt, or about 3/4-teaspoon per stick. But it may be half that for another brand or in another part of the country. So you can wind up pretty easily not knowing how salty your finished dish will be.
There are some recipes for which you would only use unsalted, such as buttercreams or butter sauces. For most baking, however, you can use salted or unsalted butter. Most bakers prefer unsalted butter, though, because it gives them more control over the amount of salt in the recipe.
Salt was originally added to butter as a preservative, so in times past, unsalted butter was quite likely to also be fresher butter. At the rate at which products fly off grocery store shelves now, it should not be a problem, although we have found some unsalted organic butter past its peak in two large stores where the high-volume turnover is in nonorganic butter.