Bellossom
Bellossom puts nearby opponents to sleep with Sleep Powder.
Bonsly
Bonsly will use Tackle. But before that you have some time to pick it up and throw it. You won't be able to throw it quite far but if you hit someone you will damage your opponent a lot, 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 drop some trophies (not assist trophies).
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 uses Explosion. One modification they've made in this pokémon is that it might not burst when released.
Entei
Entei will use Fire Spin to trap opponents into a fire vortex.
Gardevoir
Gardevoir uses Barrier. It 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 with Overheat.
Gulpin
Gulpin will swallow an enemy with Stockpile and if the character swallowed hasn't escaped, Gulpin will spit him with Spit Up.
Ho-Oh
Ho-Oh will fly behind the stage and use Sacred Fire, throwing a column of fire on the stage.
Jirachi
Jirachi is so rare that when you release it, it will drop stickers.
Kyogre
Kyogre uses Spout, a move that doesn't cause any kind of damage but that pushes the enemies off the screen with incredible force. The only way to inflict damage with Kyogre is if anyone comes into contact with it.
Latios & Latias
They both use Aerial Ace to knock enemies off the stage.
Lugia
Lugia will fly behind the stage and use Aeroblast.
Manaphy
Manaphy uses Heart Swap, an attack that makes two players switch control between the characters they chose. Don't try to commit suicide while controlling your opponent's character because it will count as a self-destruct. You will eventually regain control of the character you chose, so don't worry.
Meowth
Meowth uses Pay Day, firing coins slowly.
Metagross
Metagross uses a combination between Earthquake and Stomp. With Earthquake it buries the enemies in the ground and with Stomp it launches them away.
Mew
Mew will probably do nothing as in SSBM, but it is so rare that when you release it, it will drop CDs.
Moltres
Moltres uses Overheat as Groudon. If you touch it you'll burn.
Munchlax
When Munchlax appears on the stage, it will slowly walk around, eating any item it encounters on the stage. The moves it uses are Stockpile and Swallow. It can eat bombs without making it blow up which is good at least.
Piplup
Piplup uses a Surf move to wash away competitors on the stage.
Snorlax
Snorlax will again fall from the sky with Body Slam and crush competitors as he did in Super Smash Bros. Melee.
Staryu
Staryu will chase one opponent and start firing the move Swift at the enemy chased.
Suicune
Suicune will now use Ice Beam. After a short pause, a narrow beam of ice will jolt forward and disappear. Contact with the beam is generally a one-hit KO.
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
Torchic will use Blaze. It will stand stationary with a circular field of flames around its body. Contact with the flames will pull the opponent in and cause constant damage. Just before Torchic disappears, it will shoot opponents out of the flames with decent strength.
Weavile
It uses False Swipe by quickly dashing back and forth between two points on the ground. Enemy contact with Weavile will cause the enemy to take 1% damage and suffer the same effect as a broken shield. In this state, Weavile continues to deal 1% damage with each touch until it disappears.
Wobbuffet
Uses Counter; if you hit it, it will become agitated, hitting anyone who comes closer.