Jets and outflows are an integral part of the star formation process. While there are many detailed studies of molecular outflows towards individual star-forming sites, few studies have surveyed an entire star-forming molecular cloud for this phenomenon. The 100-deg2 Five College Radio Astronomy Observatory CO survey of the Taurus Molecular Cloud provides an excellent opportunity to undertake an unbiased survey of a large, nearby, molecular cloud complex for molecular outflow activity. Our study provides information on the extent, energetics and frequency of outflows in this region, which are then used to assess the impact of outflows on the parent molecular cloud. The search identified 20 outflows in the Taurus region, eight of which were previously unknown. Both 12CO and 13CO data cubes from the Taurus molecular map were used, and dynamical properties of the outflows are derived. Even for previously known outflows, our large-scale maps indicate that many of the outflows are much larger than previously suspected, with eight of the outflows (40 per cent) being more than a parsec long. The mass, momentum and kinetic energy from the 20 outflows are compared to the repository of turbulent energy in Taurus. Comparing the energy deposition rate from outflows to the dissipation rate of turbulence, we conclude that outflows by themselves cannot sustain the observed turbulence seen in the entire cloud. However, when the impact of outflows is studied in selected regions of Taurus, it is seen that locally outflows can provide a significant source of turbulence and feedback. The L1551 dark cloud which is just south of the main Taurus complex was not covered by this survey, but the outflows in L1551 have much higher energies compared to the outflows in the main Taurus cloud. In the L1551 cloud, outflows can not only account for the turbulent energy present, but are probably also disrupting their parent cloud. We conclude that for a molecular cloud like Taurus, an L1551-like episode occurring once every 105 years is sufficient to sustain the turbulence observed. Five of the eight newly discovered outflows have no known associated stellar source, indicating that they may be embedded Class 0 sources. In Taurus, 30 per cent of Class I sources and 12 per cent of flat-spectrum sources from the Spitzer young stellar object (YSO) catalogue have outflows, while 75 per cent of known Class 0 objects have outflows. Overall, the paucity of outflows in Taurus compared to the embedded population of Class I and flat-spectrum YSOs indicates that molecular outflows are a short-lived stage marking the youngest phase of protostellar life. The current generation of outflows in Taurus highlight an ongoing period of active star formation, while a large fraction of YSOs in Taurus have evolved well past the Class I stage.