Snake, Rattle, and Roll for the Nes. Strange concept for a game. You were a bouncing snake head that ate balls shooting out of a box to make your tail grow. Jumping in the water made, as I recall, a foot or something attack? You needed to jump up platforms and levels to get to the finish.
Pocky and Rocky 2 for the Snes. A game where you, a shinto priestess named Pocky, journeyed through the lands picking up keys to open treasure chests to random goodies. You threw endless anti-evil spell papers at enemies while your companion did the same when they saw an enemy. (You could pick your partner, a fat man who could throw boulders, a racoon named Rocky who threw leaves, a ninja girl who threw ninja stars, or a scarecrow who threw glaves.
Vegas Stakes for the Snes. You pick a character to represent you starting out. The premise is you drive with a partner to Vegas with 1,000 bucks in your pocket and continuously play games to make more money. Options for games were slots, craps, blackjack, roulette, and poker. There was never a cap or a victory amount of money. People would also come to you with strange requests or trying to sell things, you could either make or lose money with them.
Super Mario 2 for the Snes. You started out being able to pick from Princess Toadstool, Mario, Luigi, or Toad. You simply progressed through worlds trying to beat the enemies, gather keys, unlock doors, grab cherries (for the slots game after you beat the level), etc. Your character of choice changed the abilities you could work with on each level. (Toadstool could float in the air for an extended period of time, Mario was normal, Toad was fast, and Luigi did higher, exaggerated jumps.)
Battletoads: Battlemaniacs for the Snes. You were a toad who was trying to rescue friends from the clutches of an evil broad. You simply walked through all the levels kicking ass. Levels did change though based on either floating on metal flyers, zipping through brain substances on a jet bike, etc.
Super Mario RPG: Legend of the Seven Stars for the Snes. One of my all time favorite games aside from The Legend of Zelda: A Link to the Past. You became Mario, a guy who is happy go lucky beating Bowser and saving Peach in Bowser's Castle until one day a giant sword crashes through and throws everyone out. At first Mario's quest is to find Peach. But he meets others who need his help along the way. In your rpg party, you end up with Mario, Peach, Bowser, Mallow, and Gino. Mario discovers that the bad guys have shattered 'Star Road' which makes wishes come true. If anyone can ever have wishes come true again he must restore it to it's former glory. GREAT game. I cannot emphasize how much everyone should try it.
Kingdoms: Total Annihilation for the PC. Great, cheesy computer game with an engaging story line. 4 siblings rule their respective lands and one day the father of all of them dies. The leader of the undead strikes a rebellion against his siblings and they all begin to separate and fight. You play as each of them randomly, accomplishing the mission goals given while the storyline progresses.
Nox for the PC. Probably one of the better RPG's I've ever played Pc or not. You start out as Jack, a loser who lives in a trailer park with his girlfriend. He has an orb on the top of his tv he mistakenly believes is something to help with reception. However, it actually is something more powerful. The villainess activates it, sending Jack into another dimension where he must fight his way through hordes of monsters and others to beat the woman who did that to him in order to get back home. You can pick to be a conjurer summoning animals to aid you, a wizard using mostly spells, or a warrior with great strength and little ability to learn magic. The fun key parts of the game are there are many hidden areas, you can move most things around, not much in the game is taboo to do, and it's LOADS of fun. It's a less involved version of Oblivion almost.