  The simplicial volume introduced by Gromov provides a topologically
accessible lower bound for the minimal volume. Lafont and Schmidt proved that
the simplicial volume of closed, locally symmetric spaces of non-compact type
is positive. In this paper, we present a generalization of this result to
certain non-compact locally symmetric spaces of finite volume, to so-called
Hilbert modular varieties. The key idea is to reduce the problem to the compact
case by first relating the simplicial volume of these manifolds to the
Lipschitz simplicial volume and then taking advantage of a proportionality
principle for the Lipschitz simplicial volume. Moreover, using computations of
Bucher-Karlsson for the simplicial volume of products of closed surfaces, we
obtain the exact value of the simplicial volume of Hilbert modular surfaces.
