I've pretty much played every franchise. Except for one. There is only one that I can think of that I haven't played yet. Puzzle League. I can't recall ever playing anything in the Puzzle League series. Games in the series include...
Tetris Attack - SNES
Tetris Attack - Gameboy
Pokemon Puzzle Challenge - Gameboy Color
Pokemon Puzzle League - Nintendo 64
Nintendo Puzzle Collection - Gamecube
Dr. Mario & Puzzle League - Gameboy Advance
Planet Puzzle League - DS
Puzzle League Express - DSiWare
I have played any of those. So yeah, I haven't played that series yet. However, every other franchise by Nintendo I have played. I don't like them all, but I do like most of them.
For instance, I'm not a fan of Pokemon, or anything Pokemon related. So I stay away from that now. I've played the earlier games, but they never "caught" me.
But yeah, everything else I have played. Most of them many, many, many times. I mean, multiple times by multiple of times. Some of them are even my all time favorites. Like Zelda, and Mario, and Wars, among other. I love Advance Wars. One of my favorite series ever. Of course, some Nintendo franchises I have only played once or twice. But, at the end of the day, I have played them.
So, my official answer is the Puzzle League franchise.