Fox's moves are quite clearly based on Arwing functions. Him being competent at martial arts is also a part of his character based on the fact he is a trained mercenary, it's an integral part of his back story.
Captain Falcon is pretty much the exact same deal, just replace Arwing functions and mercenary with Blue Falcon functions and bounty hunter background.
Zelda is a magic caster with ties to the goddesses, so her Smash moveset references that.
Sheik is a ninja who does ninja things, some of which was actually shown in Ocarina of Time.
Ice Climbers had their moveset based on the premise of the two player mode in their game.
Ganondorf is a big bulky demon warlock, so he uses physical attacks enhanced by demon magic.
Samus' backstory includes her being trained to be athletic to a super human degree, not hard for a Smash moveset to be based off that. Unless you mean the jet boots, but she's a futuristic bounty hunter, so that fits her character. She has tons of gadgets.
Wario was shown to be a fist-fighting brute with unorthodox physical attacks and surprising agility in Super Mario 64 DS, Wario: Master of Disguise, and Wario World, so his moveset revolves around that. The bike obviously comes from WarioWare, and the farting comes from the fact he eats garlic a lot.
R.O.B has a moveset based on the games the actual toy was used to play, and an exaggeration of the actual functions of the toy (flashing eyes and moving arms).
Don't know why you even mentioned Snake, as his sources for his moves are incredibly obvious to anyone who's played even a bit of MGS. He uses iconic weapons from the MGS franchise that he's known to use (C4's, Mines, Stinger Missiles, etc), and he uses CQC, something that he has due to being a trained mercenary and is an actual game mechanic in MGS.
Villager's moveset is based on the concept that the Villagers like to collect things in Animal Crossing, so he uses the various items a Villager can collect. His moveset also clearly implies that he's not even really "fighting", he's just a guy going about his day and having fun. His fighting is basically accidental, such as tripping and dropping a potted cactus, letting off fireworks that don't quite work right, dropping a bowling ball that's too heavy for him, etc.
WFT's moveset is based off of mini-games from Wii Fit, and the actual Yoga exercises she would teach you in the game.
Rosalina is a cosmic deity shown to have a multitude of abilities and pretty much limitless potential. In Galaxy alone, she could teleport, fly, control gravity, and turn gigantic, for example, and all of these but the final one are incorporated into her moveset in Smash. Her being able to form cosmic bangs and galaxies from her body parts really isn't too hard to believe considering the character's role and background. Star Bits and Launch Stars have a strong association with her and Luma, and her Gravitational Pull move even references the cursor from Galaxy. And while shielding is a generic mechanic for all characters, the way Rosalina casts her shield in Smash looks similar to how she does in other games. Luma's presence obviously references the integral bond Rosalina has with the Lumas, and how she protects them as much as they try to help her (a mindset actual players of the characters in Smash need to adapt in order to succeed with her). But, he also references the Co-Star Luma feature from Galaxy 2. Luma even has the spin attack as his infinite jab, which was something the Co-Star Luma could do in Galaxy 2, and much like how Luma works in Smash, the Co-Star Luma could either stay "tethered" to Mario and protect him that way, or break off from him and do his own thing, and clear the way ahead and distract enemies.
Little Mac is a boxer. He does boxing moves. Some of which he actually does in Punch-Out. Then stuff like the KO Punch, Slip Counter, and Giga Mac are specifically signature moves of his.
Bowser Jr used the clown car in the NSMB games and a variation of it in the Galaxy games. His entire moveset references clown car functions from these games.
Duck Hunt Duo I admit stretches things a bit, but his moveset largely references Duck Hunt's "sister" games. And I guess the dog has some of the characteristics of a hunting dog, which is what he was in Duck Hunt.
Pac-Man has a mix of iconic moves from his games and other iconic Namco games.
As I said before, all of the characters on the roster have very strong moveset references and ties to their original games, even if they may not always be as obvious as "Kirby inhales enemies and copies their abilities or shoots them out, so he does that in Smash too". Sometimes moves in Smash are derived from a character trait rather than an actual move they did. They FEEL like they are that character, they didn't pull things out of complete nowhere, everything had a basis that added to their uniqueness and final moveset in Smash.
I didn't mention Ness because I don't know enough about him. And I feel the reason misconceptions exist about these other characters having "moves come out of nowhere" is because other people assume they know enough about a character when they really don't.