Aspects of the electron paramagnetic resonance (EPR) spectra of C60n- fulleride ions (n = 2, 3) and the EPR signal observed in solid C60 are reinterpreted. Insufficient levels of reduction and the unrecognized presence of C120O, a ubiquitous and unavoidable impurity in air-exposed C60, have compromised most previously reported spectra of fullerides. Central narrow line width signals ("spikes") are ascribed to C120On- (n = odd). Signals arising from axial triplets (g approximately 2.0015, D = 26-29 G) in the spectrum of C602- are ascribed to C120On- (n = 2 or 4). Their D values are more realistic for C120O than C60. Less distinct signals from "powder" triplets (D approximately 11 G) are ascribed to aggregates of C120On- (n = odd) arising from freezing nonglassing solvents. In highly purified samples of C60, we find no evidence for a broad approximately 30 G signal previously assigned to a thermally accessible triplet of C60(2-). The C60(2-) ion is EPR-silent. Signals previously ascribed to a quartet state of the C60(3-) ion are ascribed to C120O4-. Uncomplicated, authentic spectra of C60- and C60(3-) become available when fully reduced samples are prepared under strictly anaerobic conditions from freshly HPLC-purified C60. Solid off-the-shelf C60 has an EPR signal (g approximately 2.0025, DeltaH(pp) approximately 1.5 G) that is commonly ascribed to the radical cation C60*+. This signal can be reproduced by exposing highly purified, EPR-silent C60 to oxygen in the dark. Doping C60 with an authentic C60*+ salt gives a signal with much greater line width (DeltaH(pp) = 6-8 G). It is suggested that the EPR signal in air-exposed samples of C60 arises from a peroxide-bridged diradical, *C60-O-O-C60* or its decomposition products rather than from C60*+. Solid-state C60 is more sensitive to oxygen than previously appreciated such that contamination with C120O is almost impossible to avoid.