An array of quantum wires is a natural starting point to realize two-dimensional topological phases. We study a system of weakly coupled quantum wires with Rashba spin-orbit coupling, proximity coupled to a conventional s-wave superconductor. A wide variety of topological phases is found in this model. These phases are characterized by ``strong'' and ``weak'' topological invariants, that capture the appearance of mid-gap Majorana modes (either chiral or non-chiral) on the edges along and perpendicular to the wires. In particular, a phase with a single chiral Majorana edge mode (analogous to a p+ip superconductor) can be realized. At special values of the magnetic field and chemical potential, this edge mode is almost completely localized at the outmost wires. In addition, a phase with two co-propagating chiral edge modes is observed. We also consider ways to distinguish experimentally between the different phases in tunneling experiments.