Bushido Blade for the Play Station (1). An awesome sword fighting game. It had no health bar, but your injuries caused your death. If you were slashed in the leg, guess what - you're not using that leg anymore. You could be injured in your arms and legs to the point that you would have to roll on the ground. It was a great game.
Chrono Trigger was awesome, but I didn't discover it for a while and my playthrough of it was on an emulator. I guess that title belongs to the oldest game I have, as well as my first and favorite: Pokemon Yellow!