  We investigate the inclusive production of prompt J/psi mesons in polarized
hadron-hadron, photon-hadron, and photon-photon collisions in the factorization
formalism of nonrelativistic quantum chromodynamics (NRQCD) providing all
contributing partonic cross sections in analytic form. In the case of
photoproduction, we also include the resolved-photon contributions. We present
numerical results appropriate for BNL RHIC-Spin, the approved SLAC fixed-target
experiment E161, and the e^+e^- and gamma gamma modes of TESLA. Specifically,
we assess the feasibility to access the spin-dependent parton distributions in
the polarized proton and photon. We also point out that preliminary data on
J/psi inclusive production taken by the PHENIX Collaboration in unpolarized
proton-proton collisions at RHIC tends to favor the NRQCD factorization
hypothesis, while it significantly overshoots the theoretical prediction of the
color-singlet model at large values of transverse momentum.
