The attachment of low-energy electrons to C-60 is studied using crossed beam reactions between an effusive beam of C-60 molecules and either a monochromatic beam of low-energy electrons or a beam of highly excited Rydberg atoms. A low-energy threshold (similar to 0.15 +/- 0.05 eV) for the attachment of free electrons is observed, indicating that s-wave capture is absent, in agreement with theoretical predictions. Resonance structures at 0.2, 1.5, 4.5, 5.5, and 8 eV are attributed to electron attachment into higher electronic states of the manifold of negative ion states of C-60. In contrast, the charge-exchange reaction rate between high Rydberg (np) alkali atoms and C-60 exhibits an n dependence similar to that observed for SF6 (s-wave capture) but has a somewhat smaller attachment rate constant. The apparent conflict between slow free electron attachment and the charge transfer data is attributed to the fact that the electric field arising from the ion core of the Rydberg atom breaks the symmetry of the electron/molecule collision, allowing direct attachment into the ground state of the negative ion with no angular momentum barrier.