I believe that Phalaenopsis which used to be in
Doritis and
Kingidium (some species in the subgenera which Bob mentioned) have 4 pollinia. I don't know anything about hybrid phals, but it is probably inherited from Phal. pulcherrima.
Here are species with 4 pollinia:
Aphyllae: wilsonii, braceana, minus etc.
Proboscidioies: lowii
Parishianae: appendiculata, gibbosa, lobbii, malipoense, parishii
Subgenus Phalaenopsis, Section Deliciosae: chibae, deliciosa, mysorensis
Subgenus Phalaenopsis, Section Esmeralda: pulcherrima etc.
p.10-11 of the following book mentions this:
Orchid Biotechnology Two - Google Books