Celebi (セレビィ, Celebi) is a fictional creature in the Pokémon franchise.
Celebi is a Psychic/Grass-type Mythical Pokémon introduced in Generation II, and is categorized within the Pokédex at #251 as the "Time Travel Pokémon". It is depicted as the guardian of the forests and possesses the ability to travel through time, though this ability is shown in the main series Pokémon games only in a secret event in Pokémon HeartGold and SoulSilver. Despite its DOJO!! description, Celebi cannot learn Fly in any game. In the National Pokédex, it is registered as #251 and it is also the last Pokémon in the Johto Dex.
As a Poké Ball Pokémon
Celebi is very special among the Pokémon who can be summoned. First, it must be unlocked: it won't appear out of a Poké Ball until all playable characters and stages have been unlocked, the sound test has been unlocked, all event matches have been completed, and the Score Display feature has been unlocked (by getting 5000 total KOs). Once that is done, the chance of Celebi appearing is 1/251 ("251" being the total number of Pokémon in existence at the time of Melee's release), just like the other "unlockable" Pokémon, Mew. (Both have a double-chance of appearing in Event 37: Legendary Pokémon, though a 2/251 chance still is not that large.)
Like Mew, Celebi's action is not an attack: Celebi gently flies off the screen a few seconds after it's summoned. Afterwards, the summoner is awarded the rare Celebi Catcher bonus for 8,000 Points. The first time this is achieved, it yields a special achievement message saying "You've encountered Celebi for the first time!" and awards the player the Celebi trophy.
Celebi, as with all other Poké Ball Pokémon, features as a collectible trophy, which must be specifically earned by encountering Celebi once during any match. This makes it one of the hardest trophies to earn, because the player must essentially play the entire game through before the 1/251 chance of Celebi appearing in a Poké Ball is put into effect, and that is a very rare occurrence indeed: throwing 251 separate Poké Balls does not guarantee one appearance by Celebi among them.
As a Poké Ball Pokémon
Celebi returns as a Poké Ball Pokémon in Super Smash Bros. Brawl. Its behavior remains the same, but instead of awarding a bonus it drops 3 trophies before flying away. After the player first sees Celebi, they will get a notice saying that they have seen it for the first time and "It is a rare event indeed".
Mew, Jirachi, and Celebi appear 1/493 of the time individually, with there being 493 Pokémon at the time of Brawl's release. However, only 492 Pokémon had been officially known at this time: thus, Celebi's summon chance gave some evidence towards the then-secret Pokémon Arceus.
Celebi appears only as a trophy and exclusively in the 3DS version of Super Smash Bros. 4.