Synthetic two-dimensional (2D) materials without layered bulk allotropes are approaching a new frontier of materials flatland, one with properties richer than those of graphene-like materials. This is the case even as only a few chemical elements and blends have shown synthetic 2D forms. While hydrogen and metals are earth-abundant and form numerous compounds, rarely are 2D materials with only robust metal-hydrogen bonds. Here, a large new family of 2D materials is found from metal hydrides by high-throughput computational search augmented with first-principles calculations. There are 110 thermally and dynamically stable 2D materials that range from metallic materials to wide-gap semiconductors. A subgroup of these materials even varies from topological insulators to nodal-loop semimetals as well as from antiferromagnetic semiconductors to ferromagnetic half-metals. Unexpectedly, these monolayers resemble graphene in an ability to form weak interlayer interaction due to the variable multicenter bonding of hydrogen that eliminates the otherwise prevalent dangling bonds, rather than the covalent bonds between stacked layers as in previously reported synthetic 2D materials. This feature will favor potential experimental synthesis of these metal hydride monolayers.