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.