I'll go by series instead of characters. ALL THE SERIES!
[collapse="ALL THE SERIES!"]
Mario Series -
Super Mario Galaxy: I remember... I got that game for Christmas. It's a magnificent game. It gets high marks in almost everything. I was going through a hard time in my life. I had a disease. This game cheered me up until doctors could properly identify it and thus cure it. This game has a special place in my heart for that alone.
Honorable Mentions: Super Mario 64, Super Mario Sunshine, Super Mario Galaxy 2, Super Mario 3D World, New Super Mario Bros, Mario Kart Double Dash!!, Mario Kart Wii, Paper Mario and the Thousand Year Door, Super Paper Mario, All Mario and Luigi games, Mario Power Tennis
Yoshi Series - Yoshi's Island DS: Yeah, yeah I know. People hate it. But I like it. It's pretty fun and entertained me quite a bit when I was younger. Though to be fair, the only other Yoshi games I've played are Yoshi's Story and Yoshi Topsy Turvy.
Honorable Mentions: Yoshi's Story
Donkey Kong Series - Donkey Kong Country Returns: Tropical Freeze: I haven't gotten into Donkey Kong as much as I should, but the games I have played, I've enjoyed. I'm playing through Tropical Freeze Right now. It's one of the best platformers I've played. Quite amazing in every way. I always thought David Wise was a bit overrated. Then I played this game. Man, everything is so pretty.
Honorable Mentions: Donkey Kong Country, Donkey Kong 64,
Wario Series - Wario Ware Smooth Moves: I borrowed this game on a whim. I had no idea what I was getting into. My gosh. The game was weird, but addicting and fun! It's so zany and hilarious. The whole thing is loaded with charm. It made me a fan of the series and to this day remains my favorite.
Honorable Mentions: Wario Land 4, Wario Ware: Mega Microgames, Game & Wario
The Legend of Zelda Series - The Legend of Zelda : Wind Waker (HD) : THIS ONE WAS SO HARD. I could have put like five games here. The Zelda series is filled with amazing games and stories but I had to pick Wind Waker. It's amazing. The sense of adventure is overwhelming. The plot, the music, the characters. It's all so wonderful. Not to downplay any other Zeldas though. They're certainly amazing as well.
Honorable Mentions: The Legend of Zelda: Ocarina of Time, The Legend of Zelda: Majora's Mask, The Legend of Zelda: Minish Cap, The Legend of Zelda: Four Swords Adventure (if you can get people to play it with you, it's jaw droppingly amazing) The Legend of Zelda: Twilight Princess, The Legend of Zelda: Spirit Tracks, The Legend of Zelda: Skyward Sword, The Legend of Zelda: A Link Between Worlds
Metroid Series - Metroid Prime: This is another hard one. Metroid has tons of great games, but I had to go with the first one I really sunk my teeth into. Metroid Prime not only introduced me to 3D Metroid, but to FPS as well. To this day, it remains one of the best. A masterpiece.
Honorable Mentions: Super Metroid, Metroid Fusion, Metroid Prime 2: Echoes, Metroid: Zero Mission, Metroid Prime 3: Corruption
Kirby Series - Kirby Super Star Ultra: THIS WAS REALLY HARD AS WELL. I have to go with the one that I sank hundreds of hours into. The first game I 100% completed. It's addicting. In every way.
Honorable Mentions: Kirby Air Ride, Kirby's Return to Dreamland, Kirby Triple Deluxe
Star Fox Series - Star Fox Assault: WHAT?!?! WHY DIDN'T YOU PICK 64?!? GRUMBLE GRUMBLE... Assault has better multiplayer. This is a game me and my friends can play for hours. Single Player is great too, but it's too short...
Honorable Mentions: Star Fox 64
Pokemon Series - Uh.... Pokemon Emerald?: Too many to choose from. I'm just going to have to go with the one I sank over 999 hours into as a child. I do enjoy them all though.
Honorable Mentions: Pokemon Fire Red, Pokemon XD: Gale of Darkness, Pokemon Platinum, Pokemon White, Pokemon Black 2, Pokemon X, Pokemon Mystery Dungeon: Explorers of Sky
F-Zero Series - F-Zero: GX: I've only played two games in the series. X and GX. GX was the better of the two. It's a hard game though...
Honorable Mentions: F-Zero X
Mother Series - Earthbound?: I haven't played any of them, though I bought Earthbound recently. So I guess this will be there soon.
Ice Climber Series - Ice Climber: Haven't played it aside from a demo. Not that great honestly.
Fire Emblem Series - Fire Emblem Awakening: This honestly changes on my mood. Path of Radiance also goes here. I haven't played a lot of the games, but most of them were awesome! I'd recommend the series to everyone.
Honorable Mentions: Fire Emblem: Path of Radiance, Fire Emblem: Sacred Stones
Game & Watch Series - None: Haven't played any of them.
Kid Icarus Series - Kid Icarus Uprising: Only one I've really played. I'm dabbling in the original, but it's nowhere near as good as Uprising.
Pikmin Series - Pikmin 2: Another hard one. All three of them are masterpieces. I just gotta go with the one with the best multiplayer and most relaxing atmosphere.
Honorable Mentions: Pikmin, Pikmin 3
R.O.B. Series - None: Haven't played them.
Animal Crossing Series - Animal Crossing New Leaf: Only one I've really sunk my teeth into. I just bought it a week ago. It's pretty nifty.
Sonic Series - Sonic Generations: Also incredibly hard. I had to go with the one that compiled the best parts of the series into one game. It's Smash for Sonic and its game play is superb.
Honorable Mentions: Sonic 3 & Knuckles, Sonic Adventure (DX), Sonic Adventure 2 (Battle), Sonic Heroes, Sonic Advance 3, Sonic Colors
Metal Gear Series - None: Haven't played them. I can never find them. T.T
Wii Fit Series - None: Haven't played them. Probably should to loose weight.
Punch Out!! Series - Punch Out!! (Wii) : Only one I've played though it's amazing. So hard to find though.
Xenoblade Series - Xenoblade Chronicles: Only game is it's series. Tis a masterpeice and one of my favorite Wii games.
Mega Man Series - Mega Man 9: I bought this on a whim. Best whim ever. It's a timeless classic that shows that the old formula really does work.
Honorable Mentions: Mega Man 2, Mega Man 10
Pac-Man Series - Pac-Man: Only game I've played in the series. It's freaking Pac-Man.
Nintendo DS - Lol: Lol
Electroplankton - None: Don't plan on ever playing this series.
Pilotwings Series - Pilotwings: I played it once. For two minutes. I want to try Resort though.
Nintendogs Series - Nintendogs: Dachshund and Friends: I only played one version of the first game. Dachshunds are awesome.
Find Mii Series - Find Mii II: It's literally Find Mii 2.0.Better in every way.
Balloon Fight Series - None: Haven't played them. Does Nintendoland count?
Tomodachi Series - Tomodachi Life: Doesn't have a icon yet, so this will do. It's a fun little game. Full of charm and laughter. STOP TRYING TO STEAL MY MOM, TRAVIS! RAINE SAGE IS ENOUGH FOR YOU!
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I may add more when more series are shown officially.