First we prove a version of the Strong Half-Space Theorem for minimal surfaces with bounded curvature in $\R$. With the techniques developed in our proof we give criteria for deciding if a complete minimal surface is proper. We prove a mixed version of the Strong Half-Space Theorem. Turning to $3$-dimensional manifolds of bounded geometry and positive Ricci curvature, we show that complete injectively immersed minimal surfaces with bounded curvature are proper and as a corollary we have a Half-Space Theorem in this setting. Finally we show an application of the maximum principle for nonproper minimal immersions in $\R $.