  We have observed 104 gravitationally-lensed quasars at $z\sim1-4$ with
Herschel/SPIRE, the largest such sample ever studied. By targeting
gravitational lenses, we probe intrinsic far-infrared (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 percent (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 $38^{+12}_{-5}$ K. By applying the radio-infrared correlation, we find no
evidence for an FIR excess which is consistent with star-formation-heated dust.
We derive a median magnification-corrected FIR luminosity of
$3.6^{+4.8}_{-2.4}~\times 10^{11}~{\rm L_{\odot}}$ and median SFR of
$120^{+160}_{-80}~{\rm M_{\odot}~yr^{-1}}$ for 94 quasars with redshifts. We
find $\sim10$ percent of our sample have FIR properties similar to typical
dusty star-forming galaxies at $z\sim2-3$ and a range of SFRs $<20-10000~{\rm
M_{\odot}~yr^{-1}}$ 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 $<15$ percent
of those sources classified as powerful radio galaxies.
