Q:

How many Legendary Pokemon are in X and Y?

In Pokemon Black 2 and White 2, there were a lot of legendaries, not just from Unova but from other regions as well.  I know that Yveltal (I am playing Y version), Mewtwo and the legendary birds are in the game.  Are there other legendary Pokemon in the game other than those 5?  

A:

Okay, there are seven regular legendaries in the game(s).
The three "letter" (I just made this term up myself) legendaries are:

Xerneas - Only obtainable in Pokemon X
Yveltal - Only obtainable in Pokemon Y
Zygarde

You can also catch Mewtwo, which can be evolved into Mega Mewtwo X/Y.
And finally, you can get one of the roaming, legendary bird trio:

Articuno (if your starter is Chespin)
Zapdos (if your starter is Fennekin)
Moltres (if your starter is Froakie)

A method for catching the roaming legendaries can be found here. It's not the same as earlier generations.

