Full-band atomistic quantum transport simulations based on first principles are employed to assess the potential of band-to-band tunneling FETs (TFETs) with a 2-D channel material as future electronic circuit components. We demonstrate that single-layer (SL) transition metal dichalcogenides are not well suited for TFET applications. There might, however, exist a great variety of 2-D semiconductors that have not even been exfoliated yet; this paper pinpoints some of the most promising candidates among them to realize highly efficient TFETs. SL SnTe, As, TiNBr, and Bi are all found to ideally deliver ON-currents larger than 100 mu A/mu m at 0.5-V supply voltage and 0.1 nA/mu m oFF-current value. We showthat going from single to multiple layers can boost the TFET performance as long as the gain from a narrowing bandgap exceeds the loss from the deteriorating gate control. Finally, a 2-D van der Waals heterojunction TFET is revealed to perform almost as well as the best SL homojunction, paving the way for research in optimal 2-D material combinations.