The $\mathrm{C}-\mathrm{C}$ bond length is maximum in:

In diamond, all carbons are $\mathrm{s}{\mathrm{p}}^3$ hybridised and hence bond lengths are similar to carbon-carbon single bonds.
Graphite, ${\mathrm{C}}_{70}$ and ${\mathrm{C}}_{60}$ forms of carbon have delocalisation of electrons which leads to double bond characteristics. Hence, their bond lengths are in between carbon-carbon single and double bonds.
Hence, diamond with only single bond character will be have the longest bond.