What Pokemon are canonically unique? I really don't like the fact that many legendary Pokemon are common place in the anime and am curious as to which are truly special in the show. Is the same true in the games? I mean yes multiple people can own a legendary and battle each other but I mean in the story of the games have they ever addressed multiples?

I personally know there are multiple
>Mewtwos
>Lugias
>Bird Trios
>Genesects

I don't watch or play religiously so I am sure there are a ton.