We consider the production of two Higgs bosons in association with a gauge boson or another Higgs boson at the hadron colliders. We compute the cross sections and distributions for the processes p p →H H H and H H Z within the standard model. In particular, we compute the gluon-gluon fusion one-loop contributions mediated via heavy quarks in the loop. It is the leading order contribution to p p →H H H process. To the process p p →H H Z , it is next-to-next-to-leading-order (NNLO) contribution in QCD coupling. We also compare this contribution to the next-to-leading-order (NLO) QCD contribution to this process. The NNLO contribution can be similar to NLO contribution at the Large Hadron Collider (LHC), and significantly more at higher center-of-mass energy machines. We also study new physics effects in these processes by considering t t H , H H H , H H H H , H Z Z , and H H Z Z interactions as anomalous. The anomalous couplings can enhance the cross sections significantly. The g g →H H H process is specially sensitive to anomalous trilinear Higgs boson self-coupling. For the g g →H H Z process, there is some modest dependence on anomalous H Z Z couplings.