The short and simple answer is YES. Carbon itself holds carbon atoms, which can be combined with other elements to create explosive materials. Carbon is one of the more common elements, having either trace or large amounts in just about everything.
Carbon itself can be mixed with nitrogen to make explosive materials. There are links in the atoms that are considered unstable and could release large amounts of energy when they are broken. Most items that contain carbon are flammable and should be used cautiously.
They will release different gasses when burned. There is usually a distinct smell of the liquid forms when nitrogen and carbon are mixed. However, the solid type of the explosive normally does not contain an odor.
Items such as wood, oil, natural gas, and plants are all carbon-based items that will burn, or can be mixed with other elements and gasses to form more explosive type materials.