We investigate the limiting mechanical tension (negative pressure) that liquid water can sustain before cavitation occurs. The temperature dependence of this quantity is of special interest for water, where it can be used as a probe of a postulated anomaly of its equation of state. After a brief review of previous experiments on cavitation, we describe our method which consists in focusing a high amplitude sound wave in the bulk liquid, away from any walls. We obtain highly reproducible results, allowing us to study in detail the statistics of cavitation, and to give an accurate definition of the cavitation threshold. Two independent pressure calibrations are performed. The cavitation pressure is found to increase monotonically from -26 MPa at 0 degrees C to -17 MPa at 80 degrees C. While these values lie among the most negative pressures reported in water, they are still far away from the cavitation pressure expected theoretically and reached in the experiment by Angell and his group [Zheng, Science 254, 829 (1991)] (around -120 MPa at 40 degrees C). Possible reasons for this discrepancy are considered.