for sure, we only know there are more than one Celebi, Shaymin, and Lugia.
Many Celebi came out of the sky in the end of Pokemon 4ever, around 20-30 of them. Although, this was likely every single Celebi alive in the world today, it was still clear that there are still a few Celebi alive.
Shaymin have a big enough population to have their own traditions, and Nurse Joy wasn't particularly shocked when Shaymin was brought to her in Giritina and The Sky Warrior. It is sayed that Shaymin is the most common legendary pokemon, and that there are more than a few of them out there.
In the third episode of the Johto series, we saw a baby Lugia, Silver, be born. As he was pictured with his mother and father, and that Misty said: "This is just like the Lugia we saw in the Orange Islands." We can safely say there are at least four Lugias in the world.
Latios and Latias are also another to think about. Latios and Latias had a father, meaning that before he was killed, there was more than one. Funny their mother was never mentioned, so we can only guess that their mother is dead, otherwise their father would have kept them with her.
Mewtwo is known to be unique, because every scientist that knew how to make Mewtwo was killed by him, and the sample they cloned him from was also destroyed in the fire. There were many Mewtwo in the past, as we can hear the scientists say: "We can't lose this one." At the start of the first movie. However, there was never more than one at a time.
As for the legendary birds, we know that there are at least two Zapdos and Articuno, as they were featured in specials on TV, and guarding their islands in Pokemon 2000, while Moltres remains a mystery.
The same is said of the legendary dogs. Suicune has been seen many, many times in regular TV episodes, as well as Pokemon 4ever. As Paige has said that Suicune plays with her "All the time" we can say that there is at least one Suicune who does not travel the North Wind.
..... maybe legendary pokemon were meant to remain a mystery?