Emerging Non-Volatile Memories (eNVMs) such as Phase-Change RAMs (PCRAMs) or Oxide-based Resistive RAMs (OxRRAMs) are promising candidates to replace Flash and Static Random Access Memories in many applications. This paper introduces a novel set of building blocks for Field-Programmable Gate Arrays (FPGAs) using eNVMs. We propose an eNVM-based configuration point, a look-up table structure with reduced programming complexity and a high-performance switchbox arrangement. We show that these blocks yield an improvement in area and write time of up to 3x and 33x respectively vs. a regular Flash implementation. By integrating the designed blocks in a FPGA, we demonstrate an area and delay reduction of up to 28% and 34% respectively on a set of benchmark circuits. These reductions are due to the eNVM 3-D integration and to their low on-resistance state value. Finally, we survey many flavors of the technologies and we show that the best results in terms of area and delay are obtained with Pt/TiO2/Pt stack, while the lowest leakage power is achieved by InGeTe stack.