The PHOBOS experiment at the BNL Relativistic Heavy Ion Collider has measured the total multiplicity of primary charged particles as a function of collision centrality in Au+Au collisions at sNN= 19.6, 130, and 200 GeV. An approximate independence of Nch Npart/2 on the number of participating nucleons is observed, reminiscent of "wounded nucleon" scaling (Nch Npart) observed in proton-nucleus collisions. Unlike p+A, the constant of proportionality does not seem to be set by the pp/p̄p data at the same energy. Rather, there seems to be a surprising correspondence with the total multiplicity measured in e+e- annihilations, as well as the rapidity shape measured over a large range. The energy dependence of the integrated multiplicity per participant pair shows that e+e- and A+A data agree over a large range of center-of-mass energies (s>20 GeV), and pp/p̄p data can be brought to agree approximately with the e+e- data by correcting for the typical energy taken away by leading particles. This is suggestive of a mechanism for soft particle production that depends mainly on the amount of available energy. It is conjectured that the dominant distinction between A+A and p+p collisions is the multiple collisions per participant, which appears to be sufficient to substantially reduce the energy taken away by leading particles.