Previous results indicated that NbN thin films possess critical current and field characteristics significantly superior to that of bulk NbN having a similarTc. Further measurements made on NbN films, with thicknesses between 50 Å and 8 &mgr;, now show that, at 4.2°K, certain of these films exhibit the highest current densities of any presently known superconductor in all fields from zero up to the limit of our measurement capability (210 kOe). In addition, anomalously high current and field values have been measured in very thin (<300 Å) films. These thinner films show no depressions inJc(measured at 4.2°K) or inHc2(O) values despite decreases inTcfrom almost 16°K (in the thicker films) down to 11°K.