We study theoretically the proximity effect of a one-dimensional metallic quantum wire (in the absence of spin-orbit interaction) lying on top of an unconventional superconductor. Three different material classes are considered as a substrate: (i) a chiral superconductor in class D with broken time-reversal symmetry and a class DIII superconductor (ii) with and (iii) without a nontrivial Z₂ number. Interestingly, we find degenerate zero energy Majorana bound states at both ends of the wire for all three cases. They are unstable against spin-orbit interaction in case (i), while they are topologically protected by time-reversal symmetry in cases (ii) and (iii). Remarkably, we show that nonlocal spin correlations between the two ends of the wire can be simply controlled by a gate potential in our setup.