One of the simplest proposed experimental probes of a Majorana bound state is a quantized (2e(2)/h) value of zero-bias tunneling conductance. When temperature is somewhat larger than the intrinsic width of the Majorana peak, conductance is no longer quantized, but a zero-bias peak can remain. Such a nonquantized zero-bias peak has been recently reported for semiconducting nanowires with proximity induced superconductivity. In this Letter we analyze the relation of the zero-bias peak to the presence of Majorana end states, by simulating the tunneling conductance for multiband wires with realistic amounts of disorder. We show that this system generically exhibits a (nonquantized) zero-bias peak even when the wire is topologically trivial and does not possess Majorana end states. We make comparisons to recent experiments, and discuss the necessary requirements for confirming the existence of a Majorana state.