Bellossom
Bellossom puts nearby opponents to sleep.
Bonsly
Bonsly won't do anything unless you pick it up and throw it. You won't be able to throw it quite far but if you hit you will damage a lot your opponent, even if your opponent has less than 50% damage you may be able to knock the enemy off the screen
Celebi
Celebi will probably do nothing as in SSBM, but it is so rare that when you release it, it will give you a gift.
Chikorita
Chikorita will use Razor Leaf as in Super Smash Bros. Melee.
Deoxys
Deoxys's act is similar to the one of Ho-oh in Super Smash Bros. Melee. It will float over the stage and unleash a powerful Hyper Beam (instead of Ho-oh's Sacred Fire.)
Electrode
Electrode comes back, but it's not yet been confirmed if you will be able to carry it. One modification they've made in this pokémon is that it will probably won't burst when released.
Entei
Entei will do the same as in SSBM
Gardevoir
Gardevoir makes a big shield that doesn't allow blasts of fire guns and stuff like that to penetrate, but it does allow enemies to enter and attack from the inside.
Goldeen
Goldeen is the only Pokémon you don't want to have released from your Pokéball. It's the most useless Pokémon of all (in this series) because it only uses Splash attack, which has no effect on any characters.
Groudon
Groudon stands on the stage and burns anyone who touches it.
Ho-Oh
Ho-Oh will fly behind the stage and use Sacred Fire, throwing a column of fire on the stage.
Hoppip
Kyogre
Lugia
Lugia will fly behind the stage and use Aeroblast.
Manaphy
Manaphy uses Heart Swap, an attack that makes two players to switch the characters they control. But don't try to commit suicide while controlling they enemies character because it will count as a self-destruct. You will eventually control the character you chose again (in the same battle) so don't worry.
Meowth
Meowth uses Pay Day, firing coins slowly.
Mew
Mew will probably do nothing as in SSBM, but it is so rare that when you release it, it will give you a gift.
Munchlax
When Munchlax appears on the stage, it will slowly walk around, eating any item it encounters on the stage.
Piplup
Piplup uses a Surf move to wash away competitors on the stage.
Skarmory
Snorlax
Snorlax will again fall from the sky and crush competitors as he did in Super Smash Bros. Melee.
Staryu
Staryu will chase one opponent and start firing little stars at the enemy.
Suicune
Suicune will do the same as in SSBM
Togepi
Togepi uses Metronome, allowing it to use one of a variety of moves. Maybe the screen will become dark, making you unable to see the battle for a moment, or maybe it will put a flower on top of the head of some enemy nearby, taking some damage.
Torchic
Wobbuffet
Uses the move: Counter If you hit it, it will agitate, hitting anyone who comes closer.