I'll try to not write up a super wordy OP, but this is a pretty straight-foward premise. Your picks don't have to be the best or even your favorite games on their respective console, just a single game that you consider to be essential. For example, Halo: Combat Evolved is my favorite and most influential game on the original XBOX, but I've opted to put something else in its place.
My list is as follows:
Nintendo 64 - 1080 Snowboarding
Gameboy Advanced - Mario Kart Super Circuit
Xbox - Ninja Gaiden Black
Nintendo DS - New! Super Mario Bros.
Xbox 360 - Gears of War 3
PS3 - Uncharted: Drake's Fortune
Super Nintendo - Mega Man X
Xbox One - Sunset Overdrive
PC - Hotline Miami
Sega Genesis - Streets of Rage II
Android - Yu-Gi-Oh! Duel Links
Switch - Mario + Rabbids: Kingdom Battle
My list is as follows:
Nintendo 64 - 1080 Snowboarding
Gameboy Advanced - Mario Kart Super Circuit
Xbox - Ninja Gaiden Black
Nintendo DS - New! Super Mario Bros.
Xbox 360 - Gears of War 3
PS3 - Uncharted: Drake's Fortune
Super Nintendo - Mega Man X
Xbox One - Sunset Overdrive
PC - Hotline Miami
Sega Genesis - Streets of Rage II
Android - Yu-Gi-Oh! Duel Links
Switch - Mario + Rabbids: Kingdom Battle