What hybridization is involved in the carbon-carbon bonds?

In alkanes like ethane, carbon's orbitals are $s {p}^{3}$ hybridized - this means that one s orbital and three p orbitals come together to form four $s {p}^{3}$ hybrid orbitals. Single bonds can form between carbon atoms with other hybridizations as well ($s {p}^{2}$ with $s {p}^{2}$, for example).
In alkenes, carbon atoms can form double bonds; these bonds, consisting of one sigma and one pi bond, are formed with an $s {p}^{2}$ hybridized orbital and an unhybridized p orbital.
In alkynes, the carbon atoms can form triple bonds; these bonds, consisting of one sigma and two pi bonds, are formed with an $s p$ hybridized orbital and two unhybridized p orbitals.