  We show that the simplicial volume of a contractible 3-manifold not
homeomorphic to $\mathbb{R}^3$ is infinite. As a consequence, the Euclidean
space may be characterized as the unique contractible $3$-manifold with
vanishing minimal volume, or as the unique contractible $3$-manifold supporting
a complete finite-volume Riemannian metric with Ricci curvature uniformly
bounded from below. On the contrary, we show that in every dimension $n\geq 4$
there exists a contractible $n$-manifold with vanishing simplicial volume not
homeomorphic to $\mathbb{R}^n$. We also compute the spectrum of the simplicial
volume of irreducible open 3-manifolds.
