To make this list a bit shorter for me, I'm restricting this to "new" games I have never beaten before and games I have actually started so I have a save file somewhere.

SNES
Final Fantasy Mystic Quest
Illusion of Gaia

Playstation
Arc the Lad III
Silhouette Mirage

GBA
Sword of Mana
Shin Megami Tensei DemiKids: Dark Version

DS
Phoenix Wright
Final Fantasy XII: Revenant Wings
Shin Megami Tensei: Strange Journey
Dragon Quest IX: Sentinels of the Starry Sky

PSP
Final Fantasy Dissidia Duodecim
Metal Gear Solid Peace Walker
Persona 3 Portable
Assassins Creed Bloodlines

PS2
Shinobi
Chulips
Lupin the III: Treasure of the Sorcerer King
Suikoden Tactics
Shin Megami Tensei: Digital Devil Saga 1
Shadow Hearts
Steambot Chronicles
Front Mission 4
Zone of the Enders
Space Channel 5 Special Edition
Grand Theft Auto Vice City

PS3
Fallout 3
Valkyria Chronicles
Little Big Planet
God of War Collection
Disgaea 3
White Knight Chronicles
Demon's Souls
Mirror's Edge
El Shaddai: Tale of the Metatron
Devil May Cry 4
Penny Arcade: On the Rainslick Precepts of Darkness
Scott Pilgrim Vs the World: The Game

Wii
Mad World
Fragile Dreams
Mario Galaxy
Skies of Arcadia (GC)
Final Fantasy IV: The After Years
Phantasy Star
Ogre Battle: March of the Black Queen

Not as bad as I thought, but this list balloons when I add the games I haven't even had the chance to start...