I guess I can't do games on PC or other computers since they didn't have generations. On PC its Final Fantasy XI, on mobile its Dissidia Final Fantasy Opera Omnia.
Gen 2: River Raid (on an Atrai 7800 through backwards compatibility)
Gen 3: Kirby's Dreamland
Gen 4: Donkey Kong Country 1 or 2
Gen 5: Final Fantasy VIII
Gen 6: Final Fantasy XII or maybe Smash Bros Melee
Gen 7: Final Fantasy XIII
Gen 8 (including Wii U and Switch): Final Fantasy XV
GG/GB/GBC: Donkey Kong Land/Tetris DX/Link's Awakening
GBA: Final Fantasy I&II, IV or maybe Golden Sun: The Lost Age
DS/PSP: Animal Crossing: Wild World
3DS/Vita: Animal Crossing: New Leaf
What this tells me is that for most of these consoles, the top played games were also among my favourites or they were rpgs that often last a long time anyway. The arrival of Animal Crossing is a notable exception that gets the most play simply because it encourages you to play a little bit every day, that all adds up and I can see definitive proof on 3DS that Animal Crossing has much more playtime than anything else (about twice that of Smash Bros 3DS in second place).