  We study charmonium production at high-energy colliders (Tevatron, HERA, and
LEP2) in the framework of the k_T-factorization approach and the factorization
formalism of non-relativistic quantum chromodynamics at leading order in the
strong-coupling constant alpha_s and the relative velocity v. The
transverse-momentum distributions of direct and prompt J/psi-meson production
measured at the Fermilab Tevatron are fitted to obtain the non-perturbative
long-distance matrix elements for different choices of unintegrated gluon
distribution functions in the proton. Using the matrix elements thus obtained,
we predict charmonium production rates in gamma-gamma, gamma-p, and
deep-inelastic e-p collisions including the contributions from both direct and
resolved photons. The results are compared with the known ones obtained in the
conventional parton model and with recent experimental data from HERA and LEP2.
