My first console was the PS1 and the first game that I remember playing a ton of was Spyro the Dragon. I also had Tekken 2, Destruction Derby 2, NASCAR '99, Spyro 2: Ripto's Rage!, Tomba!, A Bug's Life, Breath of Fire III (in which I never got past the opening sequence), Frogger, Centipede, Crash Bandicoot 3: Warped, CyberSpeed, Crime Killer, Driver (in which I only played free roam), Rally Cross 2, Rugrats: The Search for Reptar, and Ridge Racer Revolution.
I wish I had managed to hold on to all of those games.
I also wore out Twisted Metal 4 at a friend's house later in the PS1's cycle, after the PS2 had been released. We would play it in his room when we couldn't play Mortal Kombat: Deadly Alliance on his step-dad's PS2 in the living room.