The NEMO-3 experiment at the Modane Underground Laboratory investigates the double-beta decay of Ca-48. Using 5.25 yr of data recorded with a 6.99 g sample of Ca-48, approximately 150 double-beta decay candidate events are selected with a signal-to-background ratio greater than 3. The half-life for the two-neutrino double-beta decay of Ca-48 is measured to be T-1/2(2v) = [6.4(-0.6)(+0.7)(stat)(-0.6)(+0.7)(syst)] x 10(19) yr. A search for neutrinoless double-beta decay of Ca-48 yields a null result, and a corresponding lower limit on the half-life is found to be T-1/2(0v) > 2.0 x 10(22) yr at 90% confidence level, translating into an upper limit on the effective Majorana neutrino mass of < m(beta beta)> < 6.0-26 eV, with the range reflecting different nuclear matrix element calculations. Limits are also set on models involving Majoron emission and right-handed currents.