If $X_0$ is a smooth projective variety over $\mathbb{C}$ such that $H^1(X_0, T_{X_0})=0$, then any deformation over a disk $D_{\epsilon}:=\{z \in \mathbb{C} | |z| < \epsilon \}$ is trivial for $\epsilon$ small enough.
Notice that in general $H^1(X_0, T_{X_0})=0$ only ensures that there are no infinitesimal deformations (i.e. deformations over Artinian rings), but the projectivity assumption ensures that nearby fibers in any flat family of projective schemes are isomorphic to $X_0$ [see Hartshorne, Deformation theory, p. 39].
For instance, the complex projective space $\mathbb{P}^n$ is globally rigid.
For other examples, one can consider Fake Projective Planes: they are globally rigid by Mostow's Rigidity Theorem. In fact, their moduli space consists of $100$ distinct isolated points.