The Hodgkin-Huxley (HH) neuron is one of the most biophysically-meaningful models used in computational neuroscience today. Ironically, the model's high experimental value is offset by its disproportional computational complexity. To such an extent that neuroscientists have either resorted to simpler models, losing precious neuron detail, or to using high-performance computing systems, to gain acceleration, for complex models. However, multicore/multinode CPU-based systems have proven too slow while FPGA-based ones have proven too time-consuming to (re)deploy to. Clearly, a solution that bridges user friendliness and high speedups is necessary. This paper presents flexHH, a flexible FPGA library implementing five popular, highly parameterizable variants of the HH neuron model. flexHH is the first crucial step towards making FPGA-based simulations of compute-intensive neural models available to neuroscientists without the debilitating penalty of re-engineering and re-synthesis. Through flexHH, the user can instantiate custom models and immediately take advantage of the acceleration without the mediation of an engineer, which has proven to be a major inhibitor to full adoption of FPGAs in neuroscience labs. In terms of performance, flexHH achieves speedups between 8×-20× compared to sequential-C implementations, while only a small drop in real-time capabilities is observed when compared to hardcoded FPGA-based versions of the models tested.