  Both charm and bottom quarks form nonrelativistic bound states analogous to
positronium. The J/psi and psi(2S) charmonium states and the first three
Upsilon(nS) bottomonium states, all spin-triplet S-wave quarkonium states below
open-heavy-flavor thresholds, have relatively large branching ratios to e- e+
or mu- mu+ pairs. In hadron collisions, experiments measuring lepton pairs can
determine polarization by using angular correlation techniques. The
polarization, in turn, can be related theoretically to the production mechanism
for the bound state. This review summarizes experimental studies with proton
beams at fixed target and colliding beam accelerators, covering a
center-of-mass energy range from 39 to 7000 GeV for nucleon and antiproton
targets. Analyses using various polarization frames and spin-quantization axes
are described and results compared. A pattern emerges that connects
experimental results over the whole energy span. The theoretical implications
of the pattern are presented and a set of new measurements is proposed.
