I'd save:
1. Metroid. I'd publicly denounce Other M as a voodoo curse, or made on a dare and not cannon. I loved Fusion, but I would have to do something so that the fusion suit goes away. Its only slightly less ugly than the PED suit.
The suits in Echos are easily my favorites. My fav games are easily Super and Echos, least being Other M and Corruption.
I think a remake a la Zero mission of Return of Samus would be so sweet. But releasing a new game in the series that is neither a retelling of the BEGINNING or a continuation after Fusion would probably just confuse people. How often to companies remake an interquel?
Well outside of Final Fantasy games anyways.
2. Zelda. Because there are still good games to be made in this series. Unfortunately this seems to be the series that they like to try out all their new motion/touch control gimmicks rather than make the excellent games they used to. Also I'm pretty much over the general direction the series has gone since Ocarina.
You spend way too much time running errands for npcs, not enough time exploring and finding stuff/solving puzzles.
Completely contradictory to my previous statement I love Majora's Mask which is mostly fetch quests, because while there are only 4 major dungeons they are excellent. The npcs are actually interesting unlike pretty much every other game after OoT, and you didn't end up going to the same locations as most Zelda games either.
I mean how many times do we need to climb death mountain, swim around lake hylia, etc.? I originally liked that they created different races like Gorons etc, but then they stopped. I mean the games have just gotten so similar to each other. Swap out the boat for a bird and you turn WW into SS. Or into a train and you have Spirit Tracks. Also how many times are we gonna go back and retcon the origin story of the master sword/gannon.
Demise is interesting but I would rather he just be a new entity like Vaati or that thing in Spirit Tracks and not some arbitrary incarnation of evil that gets reincarnated as Ganon over and over. I mean Ganon's deal used to be that he was just a thief that grabbed the triforce and it broke so he got to keep the Triforce of Power. Pretty much I was totally fine with Link to the Past being the game that established the lore. Unfortunately no one at Nintendo could think of a new plot to happen after that point since you pretty much grab the triforce and wish everything back to happy times. So they proceeded to take the series further back and further back backing away at established canon left and right. I think that in Skyward sword they even did away with Din, Nayru, and Farore in favor of a generic Angel goddess.
One of my favorite games in the series was Link's Awakening. It just had this very different tone from the games previous, and once you learned what was really happening it took on a kind of melancholy undertone that wasn't lost me even as a little kid.
So I'd probably just reboot the series from scratch.
3. Mario. Unlike the main games I actually really like Paper Mario/Mario RPGs. I haven't played Mario Galaxy 2 yet, but liked the first one. Also the only other franchises I could think of were Star Fox/F-Zero/Pikmin and I'm not super fans of those. I like them well enough, but if they got to go then they got to go. I consider Smash/Kart as spin offs. I would have picked Mario Kart as my 3rd choice based on Mario Kart 64 fulling plenty of my highschool free time with friends, but I haven't liked the ones since very much.
I would try to improve the series by making the entries more varied. My favorite games in the series are Yoshi's Island, Thousand Year Door, Super Paper Mario, Mario RPG, and SMB2. Which was just Doki Doki Panic with different player skins. Lately there has been an over saturation of the "New" SMB that frankly I haven't played other than the first one. I wasn't a fan.