  The ends of one-dimensional p+ip superconductors have long been predicted to
possess localized Majorana fermion modes. We show that Majorana end states
survive beyond the strict 1D single-channel limit so long as the sample width
does not exceed the superconducting coherence length, and exist when an odd
number of transverse quantization channels are occupied. Consequently we find
that the system undergoes a sequence of topological phase transitions driven by
changing the chemical potential. These observations make it feasible to
implement quasi-1D p+ip superconductors in metallic thin-film microstructures,
which offer 3-4 orders of magnitude larger energy scales than
semiconductor-based schemes. Some promising candidate materials are described.
