Just as the title says.

For me, the franchises are Fire Emblem, Monster Hunter, Pokemon or Shin Megami Tensei (including spinoffs like Persona and Devil Survivor)

- This is only my Nintendo side. It takes a bit more work to get me to buy other consoles (however, I am getting a PS4 due to how many JRPG's are on it/going to be released)

I bought my Wii U purely for the promise of both Pikmin and Zelda.

Smash Bros makes me buy Nintendo consoles.

Any Nintendo franchise, if they launch a system with a Mario or a Custom Robo or Kid Icarus, ect. I don't care I will buy it, because Nintendo.

Smash, Mario and Zelda

Mario Kart 8 sure forced me to get a Wii U.

Mario, Zelda,Final Fantasy,Persona,...

I dont honestly know.. its more about the combined many titles, than the 1 unique one.
With the exception of the 4 mentioned before hand, a good game in one of those franchises can be enough.

If we are talking other consoles, my requirements are:

At least 4 Tales of/Atelier games combined for me to care about other systems.

at least 5 game i want to play in : strategy/jrpg/action adventure and i buy the console.

Kingdom Hearts and Paper Mario.