We have observed 104 gravitationally lensed quasars at z similar to 1-4 with Herschel/SPIRE, the largest such sample ever studied. By targeting gravitational lenses, we probe intrinsic farinfrared (FIR) luminosities and star formation rates (SFRs) more typical of the population than the extremely luminous sources that are otherwise accessible. We detect 72 objects with Herschel/SPIRE and find 66 per cent (69 sources) of the sample have spectral energy distributions (SEDs) characteristic of dust emission. For 53 objects with sufficiently constrained SEDs, we find a median effective dust temperature of 38(-5)(+12) K. By applying the radioinfrared correlation, we find no evidence for an FIR excess that is consistent with starformation- heated dust. We derive a median magnification-corrected FIR luminosity of 3.6(-2.4)(+4.8) x 10(11) L circle dot and median SFR of 120(-80)(+160) M circle dot yr(-1) for 94 quasars with redshifts. We find similar to 10 per cent of our sample have FIR properties similar to typical dusty star-forming galaxies at z similar to 2-3 and a range of SFRs <20-10 000M circle dot yr(-1) for our sample as a whole. These results are in line with current models of quasar evolution and suggests a coexistence of dust-obscured star formation and AGN activity is typical of most quasars. We do not find a statistically significant difference in the FIR luminosities of quasars in our sample with a radio excess relative to the radio-infrared correlation. Synchrotron emission is found to dominate at FIR wavelengths for < 15 per cent of those sources classified as powerful radio galaxies.