Depends on the Pokemon. Some like Mewtwo and Deoxys had a unique origin. Some, like all 5 legendary birds, are possibly the same species. Some, like Mew, are a species with several surviving members. And Celebi can time travel and therefore be in multiple places at once.

also, if you're going to pull out the anime card, Lugia had a child, so legendaries CAN breed.

http://www.smogon.com/cap/pokemon/

some really good ideas here

The anime is stupid, and you can only have one of each bird.

Saying something's stupid doesn't justify it's right. Phione can have kids and it's a legendary.

Correction, Rotom: You can only 'catch' one of each bird. I can have several legendary birds in my game if I trade. The only Pokemon that are canonically unique are:

Arceus
Mewtwo
Mew
Dialga
Palkia
Giratina
Azelf
Mesprit
Uxie

Even Mew can be debated.

I'm pretty sure they can "breed" more Mewtwo, since he's one of the first man-made pokemon, along with Porygon.

Broken_luck, that raises a good question. Though the games won't let you do it, because Nintendo obviously doesn't want you to, in a world based on the games where Pokemon were real, I wonder if you could breed a Mewtwo with a Ditto?

Except Mewtwo wasn't bred, he was constructed. In essence, he was made almost completely from scratch with just a fragment of DNA as a base. If you want to get technical, I sure any of these Pokemon could be made by humans given enough time and money.

But considering that Mew exists, don't you think it would've been simple to breed it with Ditto?

notice the quotations, goji. :P

It's not breeding if it's not breeding :P