We present the results of a successful search for outflows associated with low-mass young stellar objects (YSOs) in a sample of 41 small Bok globules. This search was performed in the (CO)-C-12 J = 1-0 spectral line using the new multibeam receiver (QUARRY) of the Five College Radio Astronomy Observatory. We found new outflows in about one-third of the sample (14 of 41). In addition, we found five globules to be rotating, with velocity gradients in the range 0.1-0.7 km s-1 arcmin-1. The presence of an outflow was found to be correlated with the value of the IRAS-based spectral index (between 12 and 25-mu-m) of the YSOs. Outflows were not detected in most globules whose IRAS point sources had spectral indices consistent with T Tauri or older stars. We infer that outflows occur during a fairly early stage of the star formation process when the YSOs are still deeply embedded in gas and dust. Globule YSOs with outflows have gas velocity dispersions significantly larger than globules without outflows. Thus, the good mechanical coupling observed to exist between the outflow and the ambient cloud seems to support the idea that outflows can be responsible for a variety of effects, including cloud support, dispersal, or the end of accretion onto the forming star. Both the outflow spatial and velocity extents and our outflow detection rate imply an outflow duration of approximately 10(-5) yr.