Celebi

Celebi is super-rare legendary Pokémon that first appeared in Pokémon Gold and Silver, analogous to Mew in Gold and Silver's predecessors Pokémon Red and Blue. The name Celebi has numerous possible origins, such as "celery" (which is weird, since its head kinda looks like an onion) and "bee", or perhaps "celestial being".

According to the Pokédex, Celebi wanders through time, spreading forests. The Pokédex also says it "leave[s] behind an egg it brought from the future"—which is somewhat mysterious, since the egg and what hatches from it is never elaborated on. According to legend, Celebi's appearance ensures a bright and shining future.

It is considered the guardian of the forest and the Ilex Forest Shrine in Johto's Ilex Forest exists to honor it.

Thanks to time travel paradoxes and general time travel weirdness, it is unknown whether there is one single Celebi (in the same way there is one Mewtwo and one Jirachi), or whether there are actually numerous Celebi. In the Pokémon Movie Pokémon 4Ever, several Celebi appear at once. These could either be different Celebi, or actually the same Celebi coming to one point in time from different points in time. Ow, my head.

Availability
Like Mew and Jirachi, Celebi is a promotional Pokémon available mainly by attending promotional Nintendo events, or through other promotional means.

Pokémon Crystal
Celebi can be caught in Pokémon Crystal when you obtain a GS Ball at a Nintendo promotion. Show the ball to Kurt, the Poké Ball expert, and he'll tell you to leave it as an offering in Ilex Forest. Upon leaving it at the Ilex Forest Shrine, a level 30 Celebi will appear. Like other legendary Pokémon, if you defeat it instead of catching it, you'll never have another chance.

Pokémon Colosseum
Celebi could be caught in the Japanese release of Pokémon Colosseum if the player had the bonus disc, and after purifying every Shadow Pokémon. (For the US release however, Jirachi was on the bonus disc.)