Thinking back, if I define killer app as a specific game that compels me to buy a console or game device just to play it, and by extension, means I would not have bought said console/hardware had that game not been available, there really isn't a single one. I've used some games as an excuse to pick up additional platforms during a generation which is a habit I've dropped (no time to play everything).

Granted, I've used various games as the kick starter to buy into hardware platforms for nearly every generation which generally isn't the one game that I remembered above all others (and likely played the most) on that platform.

Interesting thing is it's always on secondary consoles that have that one or two games that makes me buy that console in the first place. Killer apps never sell me on a primary gaming platform; it's always the franchise collection and potential library.

NES: none. Mega Man 2, Bionic Commando, 1943, Metroid
SNES: Street Fighter II, Link to the Past, Super Metroid, Chrono Trigger
Genesis: Master of Monsters, Gain Ground
N64: none. Shadows of the Empire
PS1: none. Tekken, GT, Resident Evil, Metal Gear Solid
PS2: none. GT, Metal Gear Solid
PS3: none. Uncharted Trilogy
Wii: Wii Sports (seriously), Wii Fit, No More Heroes
XB360: Gears of War, Halo
PS4: none.
Nintendo Switch: Zelda

Scalebound got me to buy a..... Wait a minute.... Damnit!

I have some Nostalgia games but those only go back to N64 and the numerous NES and SNES games I played via emulator long after the consoles were dead. Even my N64 I only got after the GC was already released^^

The cancer will certainly continue and it's gonna get worse. I already can't even play RL on 60fps anymore. Other games at 60fps should be alright though. And maybe next gen consoles will be able to do that.

Mario Kart 64

Mario Kart Double Dash

Mario Kart Wii
Mario Kart 7
Mario Kart 8
Mario Kart 8 Deluxe

yeah, I'm a sucker for MK series.

This only really applies to older console generations, since these days I never buy a console based on just one or two games. However, back in the PS1 and PS2 days it was a bit different.

PS1: Final Fantasy VIII. Pretty much sold me on the system the first time I saw the game being played at a friends house. Tekken 3 was the secondary reason.
PS2: Final Fantasy X. I just went where the series went at this point.

PS1: FF8

PS2: Playstation 1 + FF10 (for my siblings)

PS3: Playstation 1+2

PS4: Playstation 3

I'd say it was FF but then, I've never bought a console on around the time of a FF release.

For this gen it was Dragon Age and if they take this long to release the next Dragon Age game, it'll be for the next entry too.

N64: Banjo Kazooie
PS2: Final Fantasy X
360: "The 360 is free if you spend more than $700 on a PC"
WiiU: Super Mario 3D World
3DS: Super Smash Bros. on the go
PS4: "Here's the uncharted bundle for only $200"

Starting from the 7th gen:

DS: Advance Wars Dual Strike and the Ace Attorney series.
PSP: Many ports of games I loved or wanted to try at some point, like Valkyrie Profile, the first two Star Ocean, first Lunar and The Legend of Heroes series come to mind.
PS3: Fond memories of PSOne and PS2, justified only by Valkyria Chronicles, Eternal Sonata and Resonance of Fate for a long time.
Xbox360: Lost Odyssey and Blue Dragon.
Wii: TLoZ Twilight Princess, The Last Story and Fire Emblem: Radiant Dawn
Wii U: Mario Kart 8 + the promise of a Fire Emblem x SMT crossover, later unveiled as Tokyo Mirage Sessions #FE
3DS: The chance to keep playing Ace Attorney and Professor Layton (a nice discovery in the latest years of my DS)
Vita: Persona 4 Golden and Ys: Memories of Celceta.

Gameccube - Wind Waker and it's still my favourite Zelda game

Wii U - Splatoon, if this game never came out I would of never considered buying a Wii U but I'm glad it did as not only was it amazing I got to play a bunch of other stuff on it.

Switch - Splatoon 2, Without this I would still be waiting until sometime in 2018 to grab it at the earliest.

Vita - Gravity Rush/Soul Sacrifice.

Xbox 360 - Gears of War, i remember rushing to my store on new years eve to grab this :)

Xbox One - Gears 4, I wasn't even considering buyint it until I saw Microsoft bought the rights to Gears of War so I went straight to my closest GAME and bought it.

PS2 - Metal gear Solid 2: Sons of Liberty, Played the first game to death and loved it and this was the first game I grabbed on the paltform.

PS3 - More so it became affordable with it's first revision and I'd always enjoyed PS1/PS2, But the first games I bought with it was Little Big Planet and Mirror's Edge.

PS4 -  Xbox E3 made me buy it as it was the only next gen console that made sense after that showing, I don't thinkk it really has a killer ap or system seller but it has great third party support to make it a solid platform to have along with the majority of my friends been on it but Knack was the best game at launch if that counts.

Anything earlier was more of a family console or I just got them because there were newer as I grew up rather than for any specific games.