The NEMO-3 experiment measured the half-life of the 2νββ decay and searched for the 0νββ decay of Cd116. Using 410 g of Cd116 installed in the detector with an exposure of 5.26 y, (4968±74) events corresponding to the 2νββ decay of Cd116 to the ground state of Sn116 have been observed with a signal to background ratio of about 12. The half-life of the 2νββ decay has been measured to be T1/22ν=2.74±0.04(stat)±0.18(syst)×1019  y. No events have been observed above the expected background while searching for 0νββ decay. The corresponding limit on the half-life is determined to be T1/20ν≥1.0×1023  y at the 90% C.L. which corresponds to an upper limit on the effective Majorana neutrino mass of ⟨mν⟩≤1.4–2.5  eV depending on the nuclear matrix elements considered. Limits on other mechanisms generating 0νββ decay such as the exchange of R-parity violating supersymmetric particles, right-handed currents and majoron emission are also obtained.