I have captured Mewtwo in LeafGreen! I sent our my Lvl. 53 Snorlax, and accidentally used Strength instead of Yawn, which took away about 10%-15% of HP, then I used Yawn after taking two Psychic attacks, which left me with 6 HP. Using Swift, Mewtwo fainted Snorlax, so I sent in Blasta, my Lvl. 57 Blastoise. I used Rain Dance, while Mewtwo used Swift, which took away only about 40HP. It started to rain, and Mewtwo fell asleep. I used Surf twice, which left Mewtwo with less than 3% of health. I threw an Ultra Ball, and captured him. ^^ I now also have a Level 55 Kadabra, thanks to the Cerulean Cave.
btw, not all glitches are bad. I encountered a Pokemon that was not normally in its location- Cerulean City- and it was not just any Pokemon, but Mew! ^^ I also helped my friend catch Articuno and Zapdos.