I don't think I've bothered with F-zero... otherwise I must have hit them all at some point or another. It's hard not to have played an entry or two from all of them at some point because of how long many of them have been around. Also emulators... mustn't forget emulators.
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.
I have played a lot of Nintendo franchises and they are by far my favourite between the consoles, but I am yet to play Metal Gear Solid. As a kid I was never into those games and I'm not sure why exactly. Maybe because they weren't popular enough, but I never once played a game with snake. I have played Sonic, Mario, Mega-Man and such but never Metal Gear.
I haven't played the Animal Crossing, Pokemon, or Metroid franchise.
For Animal Crossing, I didn't discover it till later on in life. After I found out about it, I thought it be cute and wanted to get one of the games a few years back. I always liked those type of games where you strategize and have to manage and mirco-manage things in the game in order to succeed. I wouldn't mind helping my little villager get out of debt while surrounded by other unique characters.
Pokemon was something that I was into when I was a kid, but it became more of a fad to me after one year of it's initial introduction to the world in the anime. I liked the cards and the little actitivity books, but the novelty wore off afterward. (Sorry, Pokie fans.)
Metroid looked supremely confusing to me whenever I saw my aunt play. I don't even know how she could tolerate the map. All in all, it's not a bad game, maybe not the game for me. However, I can still respect Samus and what she went through in order to become the bad ass person she is today.
I haven't played Animal Crossing either, just never appealed to me. Otherwise, I've played pretty much most other Nintendo franchises. Fire Emblem is a very underrated series, in my opinion. I managed to first get into these with the GBA releases. I'm surprised at how few people have played them, which is a shame.