Gravitational waves from coalescing compact binaries are one of the most promising sources for detectors such as LIGO, Virgo and GEO600. If the components of the binary posess significant angular momentum (spin), as is likely to be the case if one component is a black hole, spin-induced precession of a binary's orbital plane causes modulation of the gravitational-wave amplitude and phase. If the templates used in a matched-filter search do not accurately model these effects then the sensitivity, and hence the detection rate, will be reduced. We investigate the ability of several search pipelines to detect gravitational waves from compact binaries with spin. We use the post-Newtonian approximation to model the inspiral phase of the signal and construct two new template banks using the phenomenological waveforms of Buonanno, Chen and Vallisneri. We compare the performance of these template banks to that of banks constructed using the stationary phase approximation to the non-spinning post-Newtonian inspiral waveform currently used by LIGO and Virgo in the search for compact binary coalescence. We find that, at the same false alarm rate, a search pipeline using phenomenological templates is no more effective than a pipeline which uses non-spinning templates. We recommend the continued use of the non-spinning stationary phase template bank until the false alarm rate associated with templates which include spin effects can be substantially reduced.