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We propose a novel class of two-dimensional (2D) Dirac materials in the MX family (M = Be, Mg, Zn and Cd, X = Cl, Br and I), which exhibit graphene-like band structures with linearly-dispersing Dirac-cone states over large energy scales (0.8-1.8 eV) and ultra-high Fermi velocities comparable to graphene. Spin-orbit coupling opens sizable topological band gaps so that these compounds can be effectively classified as quantum spin Hall insulators. The electronic and topological properties are found to be highly tunable and amenable to modulation via anion-layer substitution and vertical electric field. Electronic structures of several members of the family are shown to host a Van-Hove singularity (VHS) close to the energy of the Dirac node. The enhanced density-of-states associated with these VHSs could provide a mechanism for inducing topological superconductivity. The presence of sizable band gaps, ultra-high carrier mobilities, and small effective masses makes the MX family promising for electronics and spintronics applications.