How to catch Mew in Pokémon Red (the trainer-Fly glitch)

You can catch a wild level 7 Mew in Pokémon Red without an event: let a far-off trainer spot you, press START before they walk over, fly away, fight the Route 25 youngster with a Slowpoke, then fly back and walk onto the route again. The glitch works in Pokémon Claude Red.

Steps

1. Walk into the view of a trainer who is far away on the same route. As the "!" appears, press START before they reach you, then use FLY to leave. (A trainer at the far end of a long, straight line of sight works best.)
2. Your START button now does nothing until you win a trainer battle; the route's script is left waiting.
3. Battle the Youngster with a Slowpoke on Route 25, east of Cerulean City. Let Slowpoke be the last Pokémon you see: its Special is 21, which is Mew's internal ID.
4. Fly back to the first route and step onto it. The START menu opens on its own; close it and a wild Mew (Lv 7) appears. Catch it!

Why it works

When a trainer spots you, the game stores the upcoming battle and waits for the trainer to walk over. Opening the menu and flying away leaves that waiting script behind. The next battle overwrites the trainer bytes it will read, and the enemy's Special stat ends up used as the species of a wild encounter. A Slowpoke's Special of 21 is Mew.

Other Pokémon with the same trick

Any Pokémon's Special stat (or trainer class) becomes the encounter, so different last opponents give different Pokémon, including high-level ones.