The extraordinary SN 1997cy associated with GRB 970514 has been observed photometrically and spectroscopically for nearly 2 yr. At the time of discovery, SN 1997cy was the brightest supernova (SN) ever observed (MV</=-20.1, vhel=19,140 km s-1, H0=65 km s-1 Mpc-1). Up to the last available observations (600 days after the gamma-ray burst), the total time-integrated flux was equal to or larger than that expected from the complete thermalization of the gamma-rays produced by 2.3 M middle dot in circle of 56Co. However, starting already on day 60 the luminosity decline is slower than the 56Co decay rate, indicating that the SN ejecta was interacting with circumstellar material (CSM). The interaction appeared to weaken around day 550. The spectra of SN 1997cy are dominated at all epochs by Halpha emission, which shows at least three components of different widths, as in SN 1988Z. Several other lines with different widths are also visible, especially at early epochs. The entire light curve of SN 1997cy is reproduced by a model of the interaction of the very energetic (E=3x1052 ergs) ejecta of a massive star (25 M middle dot in circle) with the CSM, with some contribution from radioactive decays. The CSM could have been ejected with a mass-loss rate of M&d2; approximately 4x10-4 M middle dot in circle yr-1 as the progenitor star evolved from a blue to a red supergiant about 104 yr before the explosion. The lack of oxygen and magnesium lines in the spectra at nebular phases poses a problem for models requiring high-mass progenitors. The possibility that most of the core material of the progenitor has fallen onto a massive black hole so that the reverse shock dies at the inner edge of the H/He envelope is discussed.