SNES
Legend of the Mystical Ninja - unique mix of side-scrolling platformer and top-down action with minigames, humorous, tough but rewarding
Super Probotector/Contra 3 - tough as nails but oh so good, also mixing genres like the above, some of the best music on the SNES
Super the Empire Strikes Back - more for fans of Star Wars, requires high frustration tolerance; still proud I finished this as a kid
Secret of Mana
Magical Quest Starring Mickey Mouse
Turtles in Time
N64
Star Wars Shadows of the Empire - not just for fans
Saturn
Panzer Dragoon Saga - I dearly love this RPG, cinematic, awesome soundtrack; true one-of-a-kind experience, sensawunda stronk
Dragon Force - unique strategy
Story of Thor 2 - similar to a Zelda game with a variety of melee combos; pleasing audio
Three Dirty Dwarves - unique Beat-em-up for up to three players, great humor, creative boss fights, good audio; this one was stolen from me in school :-(
Die Hard Arcade - tough but fun beat-em-up
Deep Fear - Resident Evil under Water
In the Hunt - side-scrolling shooter under water
Nights into Dreams - one of a kind game, reminds me more of a racing game than anything else
Guardian Heroes - another unique title, beat-em-up with RPG elements
The Crow - just kidding, this is as awful as it gets; have a look for a laugh
Also loved Virtua Cop. Maybe could be played using touch screen? But obviously light gun is the way to go for those.
Tomb Raider - also available on PS1; when it comes to immersion this is my favourite of the series
PS1
Nightmare Creatures - moody, horror themed 3rd person melee
Front Mission - round based military mech tactics with lots of dialogue and good amount of customization and lore to explore
I mostly played racing games on it: Gran Tourismo, V-Rally, Colin McRae Rally, WRC
Tomba! or Tombi, whatever it's called, and the successor, lovely 2,5 D platformers
Deathtrap Dungeon - hard as nails 3rd person hack n slash with cool levels
Discworld Noir - great adventure if you like Pratchett. On the other hand the "regular" Discworld games are tripe. Funny, yes, but very bad as actual adventure games unless you wanna play with a walkthrough.
Ghost in the Shell - cool 3rd person shooter piloting a Tachikoma. Walk on walls and ceilings!
Einhander - unique horizontal shooter where you use big ass weapons left behind by your enemies
GB
Mystic Quest - an action variant of Final Fantasy
GBA
Golden Sun
Golden Sun: The Lost Age
Sword of Mana
I remember loving an isometric 3 D ninja game on the PS1, where your guy had two different swords, one for stealing some aspect of an emey, and the other for actually hitting stuff with. Thought it was a goemon spin-off. Anybody know the name?