We present a search for Higgs bosons in multilepton final states in pp-bar collisions at sqrt(s)=1.96 TeV recorded with the D0 detector at the Fermilab Tevatron Collider, using the full Run II data set with integrated luminosities of up to 9.7 fb-1. The multilepton states considered are two electron plus muon, electron with two muons, muon with two hadronic tau leptons, and like-charge electron-muon pairs. These channels directly probe the HVV (V=W,Z) coupling of the Higgs boson in production and decay. The muon with two hadronic tau lepton channel is also sensitive to H to tau lepton pair decays. Upper limits at the 95% C.L on the rate of standard model Higgs boson production are derived in the mass range 100 <= M_H <= 200 GeV. The expected and observed limits are a factor of 6.3 and 8.4 above the predicted standard model cross section at M_H=125 GeV. We also interpret the data in a fermiophobic Higgs boson model.