Free electron attachment in the energy range 0-10 eV and Rydberg electron transfer RET) to NF3 molecules, NF3 clusters, and NF3/Ar clusters are studied by means of negative ion mass spectrometry. The experimental results are compared with density functional theory (DFT) calculations. In the free electron experiment gasphase NF3 generates the dissociative attachment (DA) products F-, F-2(-), and NF2- appearing from a broad resonance around 2 eV, in agreement with an earlier beam experiment. The most abundant fragment, F-, exhibits a small "threshold" signal at incident energies close to 0 eV. This signal increases with the target gas temperature and is due to transitions from the neutral to the anion involving vibrationally excited states close to the intersection between the two potential energy surfaces. From the temperature dependence of this threshold signal the activation energy for the exothermic DA reaction e(-) + NF3 --> F- + NF2 is derived as E-a = 0.1 +/- 0.05 eV. Time-of-flight (TOF) analysis reveals that F- arises from a repulsive electronic state releasing the fragments with appreciable kinetic energy. Free electron attachment and RET to NF3 clusters produce undissociated cluster ions (NF3)(n-) including the monomer. In the case of free electrons they are still dominantly formed via the 2 eV resonance followed by intracluster relaxation processes. DFT calculations predict a lowering of the symmetry from C-3v to C-s on going from the neutral to the anion with one F atom substantially enlarged from the NF2 plane. The calculated (adiabatic) electron affinities are EA(NF3) = 1.71 eV and EA(NF2) = 1.18 eV. From the appearance energy in the DA experiment we derive EA(NF2) = 1.1 +/- 0.1 eV.