But according to the second movie... Zapdos, Articuno, Moltres, and Lugia are needed to keep order in the world. Should you not capture them either?
And, yet, there has been cases showing that there is more than one Lugia, more than one Zapdos, Articuno, Moltres, etc.
They are just incredibly rare.
Lugia, in the anime, has been shown to have children, and the three islands in the movie are not the same places as the Gen I games where you find the three birds, indicating that they're more than likely not the same pokemon.
It all makes for a good bit of drama to say "we need <such and such> or the world will end!" and drop the implication that there's only one of that legendary, but, in reality, it's probably not true.
Mew -- Possibly more than one. I think there are probably a few failed Mews -- genetically similar yet not quite the same as the original (the worst cases ending up as Ditto's, which contain every pokemon's DNA yet are not stable enough to retain a form unless presented with an outside stimulus).
Zapdos / Articuno / Moltres -- Multiples. Very Rare, but there's more than one. One of each on their respective islands at all times. Articunos are known, for example, to be seen by people lost in Mountain snowstorms.
Lugia -- Multiples. It has been shown in the anime to have children.
Celebi -- Only one, but able to move through time, possibly creating the illusion of many.
Latios / Latias -- I am inclined to say multiples. I don't think their birth was anything out of the ordinary -- they're just amazingly rare pokemon that happen to be powerful, as well.
Jirachi -- Most likely multiples.
Deoxys -- Shown to have multiple Deoxys, I believe, in the movie.
As for the other legendaries, there's most likely only one. I don't see how there could be two Arceus, for example.
Also, remember, Giovanni ended up using Mewtwo against Gary, and all the reaction he managed to get was a "whoa, what the heck is that kind of pokemon?" Considering that most of the legendary pokemon don't have any solid research done behind it, they're almost never very well-known, so meeting it on the battlefield would probably be met with surprise, confusion, and even, perhaps, a bit of excitement?