Carbon can exist as several allotropes, about 40 of which are known including graphite and diamond. Most of the allotropes known are amorphous, like coke, soot, activated carbon to name but a few. The allotrope present depends on the the way, and conditions under which it is made. Here are some examples of this.

Graphite and diamond are the two best known forms of elemental carbon. Their structures are summed up below.

 

Graphite
Diamond
 
Fully delocalised fused benzenoid pi system. Consists of honeycomb layers of sp2 hybridised C atoms. These layers are 3.35A apart. Graphite is black and a good conductor due to it's delocalisation. It has lubricating properties due to the ability of the layers to slide over each other.
 
Sp3 hybridised C atoms form a system of cross-linked cyclohexane chair conformers. Diamond is colourless and is the hardest substance known to man. This structure is less stable than graphite and will turn into graphite at high temperatures or under high-energy radiation.

 

This was thought to be about it until a momentus discovery in 1985 by scientists at the university of Sussex...