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 linearlydispersing Dirac-cone states over large energy scales (0.8~1.8 eV) and ultra-high Fermi velocities comparable to graphene. The electronic and topological properties are found to be highly tunable and amenable to effective modulation via anion-layer substitution and vertical electric field. The 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.