An extensive set of fast-ion diagnostics, including neutron detectors, a E∣∣B type neutral particle analyzer (NPA) and the newly built four-chord solid state neutral particle analyzer array (SSNPA) and a 16-channel Fast-ion D-alpha (FIDA) diagnostic, provides a good test-bed to study fast ion physics in the National Spherical Torus Experiment (NSTX). During combined neutral beam injection (NBI) and High-Harmonic Fast-Wave (HHFW) heating, the acceleration of fast ions is evident in all fast ion diagnostics. The neutron rate is about three times larger during the HHFW heating. A fast-ion tail above the beam injection is observed in the NPA, SSNPA and FIDA diagnostics. It is also shown that the accelerated fast ions observed by the NPA and SSNPA diagnostics mainly come from passive charge exchange reactions at the edge due to the NPA/SSNPA localization in phase space. The spatial profile of accelerated fast ions that is measured by the FIDA diagnostic is much broader than in conventional tokamaks because of the multiple resonance layers and large orbits in NSTX. The fast-ion distribution function calculated by the CQL3D Fokker-Planck code differs from the measured spatial profile, presumably because the current version of CQL3D uses a zero-banana-width model. In addition, the effects of bursting instabilities on the fast ion distribution in neutral beam heated plasmas are examined. Fishbone events generally have a minor effect on the fast ion distribution and no clear correlation is observed in the NPA and SSNPA diagnostics. However, sawteeth or the combinations of fishbones and CAEs always cause neutron rate drops up to 25% and bursts at outer chords of the SSNPA, which indicate fast ion loss. It is also observed that high energy fast ions respond earlier than low energy fast ions.