There are 5 Legendary Pokémon in the game. Legendary Pokémon are Pokémon that appear only once, and if you don't capture them on your first try, well, you're outta luck.

The term "legendary bird" was first created to mean the three, well, legendary birds. They are Articuno, Zapdos, and Moltres. Then somebody twisted the phrase around and turned it into "legendary Pokémon", which includes Mewtwo and Snorlax.

An easy way to ensure the capture of a legendary Pokémon is to save the game right before you go into battle with it. Then if you mess up in any way, you can just restart the game without saving and try again.

Also, many pages recommend saving your Master Ball for Mewtwo, because you only get one. However, ALL the legendary Pokémon, including Mewtwo, have been caught with Ultra Balls. So, if you're having trouble capturing, let's say, Zapdos, go ahead and use your Master Ball on him. You'll still be able to catch Mewtwo later.

Note: Mewtwo has been caught by ice attacks (i.e. freeze him)

Following is a listing for each legendary Pokémon and their locations.

Snorlax(1): Level 30
East of Celadon City

Snorlax(2): Level 30
West of Vermillion City

Articuno: Level 50
Seafoam Islands

Zapdos: Level 50
Power Plant

Moltres: Level 50
Victory Road(3rd level down)

Mewtwo: Level 70
Cerulean Cave/Unknown Dungeon