Legendary Pokemon of Blue
Unlike all the generations that came after Pokemon Blue, there are only a grand total of four Legendary Pokemon found in the game. These are the toughest Pokemon to capture, so you must be prepared with the proper Pokemon, Moves, PokeBalls, and Recovery Items in order to catch them.
Articuno: The Legendary Bird Articuno can be found deep inside Seafoam Islands, and is a dual Flying / Ice Type. It will be at Level 50, and knows the moves Peck and Ice Beam. Ultra Balls are best used on this Pokemon, as other balls will have the tendencies of missing and not catching it.
Zapdos: The Legendary Bird Zapdos can be found at the very end of the Power Plant, and is a dual Flying / Electric Type. It too will be at Level 50, but knows the moves Drill Peck and Thundershock. Ultra Balls also work well on this Pokemon, as well as having Ground Pokemon that aren't hurt by its moves.
Moltres: The Legendary Bird Moltres can be found deep inside Victory Road, and is a Flying / Fire Type Pokemon. It will also be at Level 50, and knows the moves Peck and the annoying Fire Spin. Like its counterparts, Ultra Balls work best on it too.
Mewtwo: The Final Legendary Pokemon Mewtwo that can be caught - outside of Mew through the Mew Glitch - can be found deep inside Cerulean Cave. Mewtwo is the highest leveled Pokemon that you can capture in the game, being Level 70. It's a pure Psychic Type that knows the moves Barrier, Recover, Swift, and Psychic. If there ever was a time to use your one and only Masterball, it would be on Mewtwo.