reaper13342 :   There are so many to list, but I will try and remember them all. 

NES:  Final Fantasy, Crystalis, Dragon Warrior series, Might and Magic series, Faxanadu, Ultima series, Willow, Legacy of the Wizard
Sega Genesis:  Phantasy Star series was awesome, Golden Axe series is more of hack and slash but still fun
SNES: Final Fantasy again, Techmo's Secret of the Stars, Knights of the Round is hack and slash but still fun, Lufia series, Secret of Evermore
    Chrono Trigger, Secret of Mana
PlayStation:  Legend of Dragoon, Final Fantasy series, Suikoden series, Ogre Battle, Valkyrie Profile, Lunar Silver Star Story Complete, Heroes
  of Might and Magic, Legend of Mana, Brave Fencer Musashi, Vagrant Story, Death Trap Dungeon, Xenogears


I know there are so many good ones out there that I can't remember, but I hope this keeps you busy for a little bit.  I didn't mention the Japanese titles since I don't speak the language and have only tried to play them

I'd like to also recommend Chrono Trigger, Chrono Cross, Legend of Dragoon, Brave Fencer Musashi, Lunar Silver Star Story Complete, Xenogears, and Secret of Mana. Belial669 pretty much covered a lot of the bases I was going to

As for plat formers, I don't know many good ones outside of the big names, but I'll try. Medieval for PSX was awesome, though I'm not sure it's what you would call a "plat former." DecapAttack for the GEN was a really unique and fun game. Claymates for the SNES (and also maybe GEN?) was a really fun plat former, and you had to solve a puzzle in between each level, though nothing difficult by any means. I can't think of any more off the top of my head, but I'll let you know if I do.

Here is a couple other good ones. Star ocean is a great game, Secret of Mana is pretty good, Chrono Trigger is a amazing game and their are a lot other amazing ones too. I recommend just going through the RPG category and reading reviews on titles that you think you may like. 

I would recommend Secret of Mana (SNES),Star Ocean,Star Ocean The Second Story (SNES,PS1),Chrono Cross (PS1),Crystalis (NES), Persona,Persona 2 (PS1),Front Mission,Front Mission 3 (SNES,PS1),Saga Frontier (PS1). There are literally tons I have not listed,SNES and PS1 usually fill that need nicely,there are some on the Genesis as well.

Disgaea is a good option. It's a Turn-based strategy RPG with no real power limit. You can level up all the way to level 9999, and even after that, you can reincarnate your character so it starts back at level 1 but with improved stats. Skills and Items can be levelled up, too!

If you haven't already,  I'd recommend Paper Mario for the n64 it'll keep you busy for a little while. It's a turn based RPG with a pretty deep plot.