THE FOLLOWING CHARACTERS ARE LISTED IN NO PARTICULAR ORDER, AND ARE MERELY STATING THEIR NITELLIGENCE RATHER THAN RANKING THEM
Mario
Mario has a PhD in medicine, as well as being a plumber, professional golfer, baseball player, tennis player, soccer player, a teacher, a hero, a fighter, janitor, airplane pilot, submarine pilot, kart racer, biker, etc. The man can do every job under the sun and do it well. It takes intelligence to know how to do all that.
Link
Most incarnations of Link start out as just a boy who's never really done anything extraordinary in his life. Suddenly one day, he's thrown into battle with a hundred different weapons that he's able to use perfectly within three seconds of obtaining them. Smart enough to learn how to use a weapon just by watching it float in the air in front of you.
Kirby
Copy ability. He knows everything his opponents know and more.
Pikachu
Sure, he's a Pokémon. Sure, he can't speak english. But then, Pokémon do not learn english as their first language and english is said to be the hardest language to learn as a second language. Perhaps Pikachu simply doesn't have the time or doesn't want to put in the effort. That said, Pikachu is likely to be the Pichu from the last game. Why? He knows Volt Tackle, and has the goggles that Pichu had in Melee. Volt Tackle is an attack that can only be learned in the Pichu evolutionary stage. Pichu decided that he was not strong enough, so he learned a strong attack, Volt Tackle, and worked to evolve. Pichu in the Pokémon games cannot evolve unless they have a trainer, yet this Pichu managed to find a way.
Princess Zelda/Sheik
Triforce of Wisdom. Sure, perhaps the Triforce doesn't grant her infinite wisdom. I never said it did. When the Door of Time is opened, the Triforce is split into three parts; Power, Wisdom, and Courage (unless there is the extremely unlikely scenario of the person opening the Door having the perfect balance of each). The three parts then enter the bodies of the people in the world that most personify them. The Triforce of Power went to Ganondorf, the great King of Evil who overthrew Hyrule. The Triforce of Courage went to Link, a little boy who, against all odds, willingly fought to save the land from darkness. The Triforce of Wisdom went to Zelda.
Princess Peach
Little is known about Peach's intelligence. She has been shown doing many of the sports that Mario does, so her intelligence may be closer to his. However, being kidnapped by the same person again and again and again leaves some to be questioned.
Samus
Samus was raised by the Chozo, bird people who's lives (as shown in the logs in the Metroid Prime series) revolved around knowledge. The Chozo wished nothing but to learn. Surely growing up with them Samus must have learned a great deal of what they know.
Mr. Game and Watch
Game and Watch is an enigma. He has been shown doing many things in the Game and Watch games. Many argue that he is just a sprite, but he is a character as well. A character intelligent enough to do a multitude of jobs.
Toon Link
He's Link. Except he's also a sailor and a musician.
Wolf
Head of the Star Wolf team, designed the Wolfen, and figured out how to survive being shot down in space.
In space.
Wario
Contrary to popular belief, Wario is actually quite intelligent. CEO of the WarioWare company, designs video games, able to repair a bike which he keeps in his pocket, and managed to build a dimensional transporter in a matter of seconds using spare items around his living room.
Yoshi
There is actually little insight on Yoshi's intelligence. There's little to say that he is intelligent, and little to say he's not. Yoshi is unknown as of this point.
Pokémon Trainer
Ten years old and manages to be able to survive on his own on a journey, finding food and shelter on said journey and also providing his Pokémon with food. Assumed to know survival skills, possibly from boy scouts.
Pit
An angel from Heaven. Heaven, the kingdom of God. God, the almighty all-knowing entity. Pit is commander of Palutena's army, so he must be fairly intelligent to be able to lead the army of the heavens.
Olimar
Able to rebuild his space ship with nothing more than the help of sentient plantlife. Also makes scientific records of the creatures on the planet during the Pikmin game.
Ness
I've never played Earthbound, so I can't say anything about Ness.
Meta Knight
Leader of the Meta Knights. Designed the Halberd. Extremely skilled with the sword. Made his cape able to turn into wings.
Marth
I've never played Fire Emblem or Fire Emblem 3, so I can't say anything about Marth.
Luigi
For the most part on par with his brother, however he's not shown to have a PhD in medicine.
Lucas
I've never played Mother 3, so I can't say anything about Lucas.
Lucario
Able to speak english (without moving his mouth for that matter). Able to use an attack that doesn't exist. Little else can be said.
Ganondorf
Great King of Evil. Conquered the kingdom of Hyrule four times (perhaps more if I'm not remembering them all). Manipulated Zant to take over the Twilight Realm and Hyrule again. Manipulated the Ancient Minister to suck the world into Subspace.
Bowser
Conquers the Mushroom Kingdom with an army of Goombas and Koopa Troopas. Built a flying castle. Managed to tape a Magikoopa onto a story book to steal the Star Rod. And it worked. Built a galaxy.
Jigglypuff
Never seems to realize that its singing is what puts people to sleep. However, is very talented at drawing mustaches.
Ike
Fights for his friends. Leads the Crimean army to defeat the Daein army which is superior to them in almost every way. Able to convince the Empress of Begnion to help save a country that is for all intents and purposes dead.
Ice Climbers
Managed to find a mountain with vegetables growing on it. However, they actually cared enough to do this.
Fox
Leader of the StarFox team. Operates the Arwing. Hears magical voices in his head while on Sauria for the first time. Does a barrel roll.
Falco
Is completely useless during actual fights in StarFox 64. Acts as though he's better than Fox when he manages to crash into Fox killing him.
Donkey Kong
Shown to live a life not too dissimilar to that of a human. Can operate a gun made of wood and coconuts. Knows how to play the bongos. Well-dressed.
Diddy Kong
Uses a jetpack made of wood. A jetpack that uses fire for propulsion. A wooden jetpack.
Dedede
Mechanized his hammer. Built a castle on a mountain. Knew better than to be the one to take Kirby's dessert in Squeek Squad.
Captain Falcon
God is all-knowing. Thus Captain Falcon knows everything.
Snake
Has an IQ of 180. Knows how to use a multitude of weapons in batle and uses them effectively.
Sonic
Makes stupid jokes at inappropriate times. Doesn't know how to swim. Races with a flying snowboard when he's fricking Sonic the Hedgehog.
R.O.B.
The Ancient Minister. Assumed to have designed the Subspace Bomb. Leads the robots of the Island of the Ancients.