I never buy a console if it only has 1 game I'm interested in but I can list the games which have been the deciding factors in my hardware purchases.
Game Boy: Wario Land: Super Mario Land 3
PlayStation 1: Gran Turismo/Tekken 3/Crash Bandicoot
Game Boy Color: Pokémon Yellow
Nintendo 64: Super Mario 64
Gaming PC: Command & Conquer: Tiberian Sun/Half-Life/Diablo 2
PlayStation 2: Gran Turismo 3
Game Boy Advance: Pokémon Ruby
Xbox 360: Dead Rising
PlayStation 3: Uncharted/Valkyria Chronicles
Wii: Super Mario Galaxy
PlayStation 4: Driveclub/The Last of Us Remastered
PlayStation Vita: Minecraft/Wipeout 2048
Nintendo 3DS: Pokémon SoulSilver
Wii U: Super Mario 3D World/Super Smash Bros. 4
Oculus Rift: Half-Life 2 VR
If Dead Rising 3+4, PvZ: Garden Warfare, Rise of the Tomb Raider and Quantum Break had stayed exclusive I'd have an XB1 as well.
Edit: 12/23 are Japanese games. More than I thought actually 
