We search for novel two-dimensional materials that can be easily exfoliated from their parent compounds. Starting from 108423 unique, experimentally known three-dimensional compounds we identify a subset of 5619 that appear layered according to robust geometric and bonding criteria. High-throughput calculations using van-der-Waals density-functional theory, validated against experimental structural data and calculated random-phase-approximation binding energies, allow to identify 1825 compounds that are either easily or potentially exfoliable, including all that are commonly exfoliated experimentally. In particular, the subset of 1036 easily exfoliable cases---layered materials held together mostly by dispersion interactions and with binding energies up to $30-35$ meV$cdottext{AA}^{-2}$---provides a wealth of novel structural prototypes and simple ternary compounds, and a large portfolio to search materials for optimal properties. For the 258 compounds with up to 6 atoms per primitive cell we comprehensively explore vibrational, electronic, magnetic, and topological properties, identifying in particular 56 ferromagnetic and antiferromagnetic systems, including half-metals and half-semiconductors.
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