  We test claims that the power-law mass functions of young star clusters (ages
$\lesssim\mbox{few}\times10^8$~yr) have physical upper cutoffs at
$M_*\sim10^5~M_{\odot}$. Specifically, we perform maximum-likelihood fits of
the Schechter function, $\psi(M)=dN/dM\propto M^{\beta}~\mbox{exp}(-M/M_*)$, to
the observed cluster masses in eight well-studied galaxies (LMC, SMC, NGC 4214,
NGC 4449, M83, M51, Antennae, and NGC 3256). In most cases, we find that a wide
range of cutoff mass is permitted ($10^5~M_\odot \lesssim M_* < \infty$). We
find a weak detection at $M_* \sim 10^5~M_\odot$ in one case (M51) and strong
evidence against this value in two cases. However, when we include realistic
errors in cluster masses in our analysis, the constraints on $M_*$ become
weaker and there are no significant detections (even for M51). Our data are
generally consistent with much larger cutoffs, at
$M_*\sim\mbox{few}\times10^6~M_{\odot}$. This is the predicted cutoff from
dynamical models in which old globular clusters and young clusters observed
today formed by similar physical processes with similar initial mass functions.
