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!
NES- Megaman 3, Crystalis, Mario 2 (Yes, Mario 2 and not 3), Castlevania 3, Dragon Quest 3, Final Fantasy 3, Sweet Home, Castlevania 3, Contra, Gargoyle's Quest 2, Ninja Gaiden
Genesis- Ristar, Strider, Sonic 3, Contra Hard Corps, Castlevania Bloodlines, Phantasy Star 4, Shining Force 2, Streets of Rage 2, Splatterhouse 3, Shinobi 3
SNES- Chrono Trigger (Best game evar), Final Fantasy 6, Megaman X, Earthbound, Clock Tower, Dragon Quest 5, Legend of Zelda Link to the Past, Demon's Crest, Killer Instinct, Super Metroid, Breath of Fire 2, Super Castlevania 4, Terranigma, Tales of Phantasia, Super Mario RPG, F-Zero, Super Bomberman
PC Engine- Castlevania X, Splatterhouse, Demon's Crash
N64- Resident Evil 2, Conker's Bad Fur Day, Ocarina of Time, Super Smash Bros, Megaman 64, Killer Instinct Gold, Bomberman 64
PS1- Resident Evil 3, Metal Gear Solid, Silent Hill, Megaman X4, Final Fantasy 9, Castlevania Symphony of the Night, Strider 2, Tekken 3, Chrono Cross, Legend of Dragoon, Xenogears, Tomba, Parasite Eve, Clock Tower 2, Crash Bandicoot 3, Spyro the Dragon, Breath of Fire 3, Dragon Quest 7, Syphon Filter
Too numerous to count. But I did enjoy playing Super Mario Land 6 Golden Coins (the game that Wario debuted in), classic Sonic The Hedgehog, Pokemon Crystal, and if I remember rightly, The Legend of Zelda: The Link To The Past.
Although I did once have many games for Playstation 2, xbox, Gamecube, Sega Megadrive II, Nintendo DS, PSP, and Gameboy Color/Advance. Unfortunate circumstances means I no longer have them. Did enjoy playing Black, GTA San Andreas, Medal of Honor, Crash Bandicoot and others.
And sometimes now Super Metroid Randomizer (It will randomize items, except Morph Ball, first Missiles, the first Super Missiles and the first Power Bombs.) The bigger Items was randomized (Not completely, it must be possible to beat the game) ^^