Phew...here we go.
Mushroom Kingdom: Lemmy&Larry, Peach, Boo.
The first two would be great if they could have their own game, I mean honestly. Peach because she has gotten to spawn so much love-triangle fanon over her decades of incidents, and Boo because, at least to me, he is the titular baddie of the series. You see a Boo or the horror theme surrounding its cuteness, and you know, every time, it's Mushking.
Pokemon: Probably popular decisions but...Buizel/Floatzel and Munchlax. Gym Leader wise, I don't really know anything about the ones past 3rd Gen, but I'd go with Erika.
I used to be one of the weasels all the time before I became a hybrid of own kind in fact zel. The latter ended up inspiring some of my RP character designs a bit too much...Runner up? I'd say the Kyo/Swampert mashup I've seen in this one fusion picture. It's really good.
You could arguably throw Royjibiv in there if you include fanmade "Fakemons."
As for Erika, it's because she's the one most stuck in my mind. I blame having an old VCR of her particular anime episode. In the games, though, she gets to show off a Japanese feel that, in my opinion, fits pretty well for the first game, being grass type and all (and the whole "sakura petals" cliche, yadda yadda).
Zelda: ....I dunno. Do the Four Swords Links count?
The only Zelda game I've seriously played through (or even seen very much of, for that matter) is Four Swords Adventures. I LOVE that game, and it does tell me I would enjoy the top-down Zeldas a lot as well, but I don't know why I never tried to.
Megaman: Okay, who put Megaman in a topic about Nintendo characters? XD But I'll say mine: Galaxy and Toad.exe.
Star Fox: Slippy.
I don't know why, but I get the feeling his antics would be more fun if another Star Fox actually happened. He isn't to be doubted though; his Landmaster skills in Assault are the best in the game, and his on-foot shots hurt too. Maybe he's just better at ground combat than the others, something that isn't seen much in this series (for obvious reasons XD).
F-Zero: Character-wise, well....I'm not sure, really. Machine-wise, either Golden Fox, White Cat, or Groovy Taxi.
The cast is pretty diverse despite not getting too much in-depth with the storylines. I can't say Falcon directly, either, because GX's story didn't make much sense at points XD (he still is amazing in Smash though). As for machines, the Golden Fox is much better past the first game and isn't as slippery as one would expect from its D grip. White Cat is pretty crazy in the GBA F-Zeroes as it really gets to show off its excellent grip in those games (which have pretty good control). Groovy Taxi because the idea is just silly overall.
This series needs to come back, like honestly.
Sonic: Again, mentioning something else in a Nintendo characters topic? XD But definitely Nack/Fang. The popgun is still a really cool thing, but I miss the guy a lot; I don't see why he can't be in the current games, given he's perfect for the cartoony side of the series.
Kirby Oh dang, that's a hard one....ummmmm.....Adelaide. (She's called something else in Dream Land 3)
Kirby 64 is the first Kirby game I ever played and one of the very first games I can claim to have 100% completion on. For that time, the painting idea still seemed pretty unique for what it was, especially given the enemies retained their sketchy structure when she threw them onto the field. Also, you don't get many allies in videogames who give you occasional free 1-ups!
Animal Crossing, Fire Emblem, Metroid, etc. Ummmmm....nothing rings a bell. Mostly because I haven't either played them or I just don't know enough. If FE classes count though, I like the dark mages in the GBA games, what with their giant kooky-looking specter sleeved robes.