We present a search for pair production of doubly-charged Higgs bosons in the processes qqbar to H++H-- decaying through H++/-- to tau tau, muon tau, muon muon. The search is performed in ppbar collisions at a center-of-mass energy of sqrt{s}=1.96 TeV using an integrated luminosity of 7.0 fb-1 collected by the D0 experiment at the Fermilab Tevatron Collider. The results are used to set 95% C.L. limits on the pair production cross section of doubly-charged Higgs bosons and on their mass for different H++/-- branching fractions. Models predicting different H++/-- decays are investigated. Assuming BR(H++ -> tau+ tau+)=1 yields an observed (expected) lower limit on the mass of a left-handed H++/-- boson of 128 (116) GeV and assuming BR(H++ -> mu+ tau+)=1 the corresponding limits are 144 (149) GeV. In a model with BR(H++ -> tau+ tau+)=BR(H++ -> mu+ tau+)=BR(H++ -> mu+ mu+)=1/3, we obtain M(H++(L) > 130 (138) GeV.