Here are some ideas I have for items and stages.
Pokémon Tower (Pokémon)
I think Pokémon Tower would be similar to the Tomodachi Life stage. The top few floors would be visible, and you could battle on the top of it. When you enter the floors below, the interior is seen. The interior has gravestones, which can be broken to reveal a Ghost. The Ghost stays in the place of the gravestone, and does damage to whoever walks into it, thus acting like Green Hill Zone's checkpoints. They will eventually disappear and their gravestone will reform. In the Omega version of the stage, you fight on top of the tower, and the ghosts fly around in the background, watching.
Distortion World (Pokémon)
Distortion World would be a stage that relies heavily on floating platforms. Some of them move up or down when stood on, and the main platform has a waterfall flowing down from it. Smokey portals also occasionally appear, allowing you to enter one and reappear on a different platform. The platforms are random each time you play the stage, and gravity is less powerful. Giratina will occasionally fly by in the background and the gravity and controls will be switched, and the stage will be flipped randomly, like in the Spear Pillar stage from Brawl.
Giygas Battle (Earthbound)
This entire stage would essentially be a giant stage hazard. Giygas would take up the entire background, and he would periodically interfere with the battle. He would shoot down lasers like in the Spear Pillar stage from Brawl, he would shake around the platforms and destroy sections, he would invert controls, etc. This stage would really be a fight to survive the longest rather than against your opponent. It wouldn't be for competitive purposes, just for fun. The Omega form would still be disturbing, with Giygas watching you and ominously shifting around in the sky. The platforms of the stage would be made of an intestine-like material, just like the path that leads up to the Giygas battle in Earthbound.
Wall Between Worlds (Zelda)
This stage would work like a basic stage like Battlefield or something, but the aesthetic is what pops out. It all takes place inside of a wall, and everybody is flat like in a G&W stage. This stage is basically just a representation of what it's like for Link to fight while in painting form in LBW. Everything has the art style of a painting, and the background is a stone wall. After a few minutes or so, the aesthetic would change from Hyrule to Lorule.
Labyrinthia Town Square (Professor Layton/Ace Attorney)
This stage takes place in the center of Labyrinthia. It has walk-off edges, and there are pedestrians walking around. Windows of buildings would act as platforms. A few minutes into the match, rain will start, and the surviving pedestrians will run inside. Lightning will strike down in the background, revealing a bell tower that comes out of the flames. If you wait a bit longer, the rain will end, the pedestrians will come out again, and some in the background will begin to study the bell tower with confusion.
These act as heal items. A normal Potion will heal a little bit, a Super Potion heals a bit more, etc. The best healing one is the Full Restore, which heals 100%.
The Thinker (Ace Attorney)
This item is an extremely heavy projectile with a fast fall speed. It does a lot of damage if dropped from above. If it's thrown down onto the head of an airborne enemy, it'll spike them. If it's smash attacked, papers will fly out.
Yo-Kai Medallions (Yo-Kai Watch)
I imagine that Yo-Kai Watch characters have to appear at some point in Smash Bros, so it only makes sense for the series to have it's own version of the Pokéball. These medallions summon a random Yo-Kai to attack. I won't go into them here, because I'm lazy.
Eggplant Wizard (Kid Icarus)
When spawned, the Eggplant Wizard would begin to throw Eggplant bombs at enemies of the one who summoned him. If one hits, that enemy becomes an eggplant with their legs still visible. They can't attack as eggplants, but they can still shield and roll. They must wait for the eggplant effect to wear off.
I used to think Maxwell had a chance to be playable in Smash because of all the Ninntendo crossovers in Scribblenauts Unlimited, but Scribblenauts Unmasked makes me think that Maxwell might be tricky ground now. But he can still work as an assist trophy! When summoned, Maxwell will pull out his notebook. He will then summon a random Pokémon, Yo-Kai, or Assist Trophy (not including himself). He's essentially an Assist Trophy that can give you better (or worse!) summons.
Spyro (Spyro the Dragon)
Spyro will spawn and begin to fly and shoot fireballs. Sparx will follow him around as a small visual detail.
Tree Rex (Skylanders)
Tree Rex will stay in one place, and slam his fists around into the ground. He will bury anybody he hits. His Woodpecker will also fly around and peck people.
Trigger Happy (Skylanders)
Trigger Happy would work similarly to the Meowth Pokéball. He'll jump up, and shoot gold coins rapidly in one direction.
Ditto will spawn, wait a moment, then transform into whichever fighter summoned him, acting like a level 5 CPU. It can be defeated by waiting for it to disappear, or by KO'ing it.
Once spawned, Tyrantrum will run around, biting as many people as possible. It will occasionally pause to breath dragon breath.
Mr. Mime will create semi-invisible moving platforms using his psychic powers. These work like normal platforms.
Machamp will run back and forth across the stage (using the animation from him as a ride Pokémon in S/M) until he runs into somebody. When he does, he'll pummel them senseless and launch them. He can bust through shields.
Marrowak will throw its bone like a boomerang, hitting enemies twice. It'll continue to jump around and throw it until it disappears.
Just like normal Marrowak, but the boomerang deals a burn effect.