Step 1: List the carbon forms.
Carbon has several forms called allotropes. The common ones are graphite, diamond and fullerene. We must find the most stable one.
Step 2: What does most stable mean.
The most stable form has the lowest energy. A lower energy form does not change into another form easily.
Step 3: Look at graphite.
Graphite has flat layers of carbon atoms. This layered build is the lowest energy form of carbon at normal temperature and pressure.
Step 4: Look at diamond.
Diamond has a strong three dimensional network. It is very hard, but its energy is a little higher than graphite, so it is slightly less stable.
Step 5: Look at fullerene and coal.
Fullerene is a ball shaped form with higher energy, so it is less stable. Coal is not a pure form of carbon at all, so it does not count as an allotrope.
Step 6: Final choice.
Because it has the lowest energy, graphite is the most stable form of carbon.\[ \boxed{\text{Graphite}} \]