For most of these I can copy from a general gaming topic a while back
(Going by the games I actually played on that system, so for example Trails in the Sky SC is better than FC, but I played that on PC, not PSP, hence FC is my best PSP game)

PC (2010s): Trails in the Sky SC
PC (2000s): Deus Ex
PC (1990s): System Shock 2

PS1: Xenogears
PS2: Ar Tonelico 2
PS3: Trails of Cold Steel 2
PS4: (for now) Ys VIII

PSP: Trails in the Sky FC
PS Vita: Ao no Kiseki

NES: Final Fantasy
SNES: Final Fantasy VI
N64: Paper Mario
Gamecube: Paper Mario: The Thousand Year Door
Wii: Xenoblade Chronicles
Wii U: Xenoblade Chronicles X
Switch: (for now) Xenoblade Chronicles 2

GB: Pokemon Blue/Red
GBC: Pokemon Silver/Gold
GBA: Super Robot Wars Original Generation 2
DS: Radiant Historia
3DS: Shin Megami Tensei IV

Xbox: Fable
XBox 360: Lost Odyssey

Mega Drive/Genesis: Phantasy Star IV
Dreamcast: Skies of Arcadia