Some people know that it's impossible to catch Mew in Pokémon Yellow, but there is a glitch you can use to add this legendary Pokémon to your Pokédex.
1. Heal your Pokémon at the Cerulean City Pokémon Center.
2. Defeat the trainers on Nugget Bridge.
3. Do not battle the trainer in the grass field to the left of Nugget Bridge, across the water, but safely walk past him without making eye contact.
4. However, in this grass field, you must find and catch an Abra in the tall grass.
5. Make sure to save your game.
6. Use Abra to teleport to your last visited Pokémon Center.
7. From the Pokémon Center, return to Nugget Bridge, but this time, after crossing the bridge, go to the right.
8. You should now be on Route 25.
9. Defeat only the bottom trainer, the 2nd from the left.
10. Remember to save your game.
11. Return to the grass field to the left of Nugget Bridge.
12. Position your character in a way that they are directly facing the trainer you avoided earlier, but ensure the trainer is just out of the screen's reach.
13. Move down one square and simultaneously press the START button.
14. The menu should appear, even though the trainer can see you.
15. Use Abra again to teleport to your last Pokémon Center.
16. Return from the Pokémon Center to Nugget Bridge, but this time, after crossing the bridge, go to the right.
17. You should now be on Route 25.
18. Defeat the top trainer, the 3rd from the right, but if you challenge him, make sure he sees you at the highest point on the screen possible, while facing right.
19. Use Abra once more to teleport to your last Pokémon Center.
20. Walk onto Nugget Bridge.
21. The menu screen should appear halfway across Nugget Bridge.
22. Close the menu screen, and Mew will appear there.
23. Lower Mew's HP and use a Poké Ball to catch the Pokémon.
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