I'll just put in my take on it via tier list. I am biased and haven't even played every series the characters are in.
Tier S
Ness - I actually never played Earthbound. I just really like the idea that Ness is this powerful.
Tier A
Kirby
Olimar with Hocotate Tech - Eternal Fuel Dynamo, Nova Blaster... this is assuming he had pocket versions. With his iconic gear, i.e. the Pikmin, he would be way down.
Pit
Ike
Link/Young Link/Toon Link - Ganon really seems stronger but his track record with Link shows.
Ganondorf
Marth/Roy - Killed Dark Dragons who were almost powerful as gods. Ike killed a real one.
Samus
King Dedede
Metaknight
Pokemon Trainer - Above all Pokemon for obvious reasons.
Tier B
Mewtwo - All pokemon are relatively ridiculous canonically, well, the fully evolved ones. Ubers are stronger but not by too much, it is not as exaggerated like in the anime.
Lucario
Charizard
Sonic
Mega Man
Mario/Dr. Mario
Luigi
Wario
Bowser
Yoshi
Tier C
Fox/Falco/Wolf - Arwings are banned, but they seem capable as long as they have gear. Never played their games.
Greninja - Great but isn't ridiculous without a Mega.
Donkey Kong
Diddy Kong - Slightly weaker than Donkey, because he has trouble damaging the fat/burly enemies in the Country games. Otherwise, they are almost identical.
Zero-Suit Samus
Captain Falcon - Don't know too much about him. Basing on the fact that he's a bounty hunter in a futuristic setting. If he had the gear, he could be pretty powerful. Not basing off of that Anime Falcon Punch meme, otherwise he'd be high A.
Snake - I'm not too certain of his capabilities, but he seems extremely resourceful.
Little Mac
Pikachu - With a lightball, it has a chance to be compared with Fully Evolved Pokes.
Tier D
Ivysaur
Ice Climbers
Wii Fit Trainer
Squirtle
Jigglypuff - I'd say basics and babies are about on par with normal humans in terms of power level.
Pichu
Peach - Can be not useless, i.e. Super Princess Peach, SMB2, but her track record as being super useless takes precedence.
Zelda/Shiek - Her incarnations can be very powerful, in theory, but just like Peach, her track record says she has potential but would rather just hide behind/inside crystals.
Tier Get Eaten Alive
Villager
Olimar with Iconic Gear - Too small to make a difference. Don't get me wrong, he can kill things 100x his size, like the size of a cat.
ROB - It's a toy. Olimar can salvage that.
Tier I have no clue
Lucas
Mr. Game & Watch
Rosalina & Luma