The Mew Glitch

Yes, this is a real glitch, I tested it myself. It is only compatible with Red, Blue, Green (as far as I know) and Yellow.

First, get a Pokémon about Level 7. I used a Level 10 Mankey. Go to the Underground Pass. At the Lavender Town end, save before going through the entrance. Leave the building. Take a step down, and press start immediately, otherwise it won't work, and you'll battle a Gambler. Fly to Cerulean City. Go up Bond Bridge, and towards the guy with a Slowpoke (remember to avoid him earlier in the game). Make sure he has to move to battle you, otherwise the game will freeze. Beat him, he has a Lv 17 Slowpoke, and fly to Lavender Town. Leave the town by the west (left) entrance.The start menu should appear.Press B and Mew appears. It is at Level 7. Although it is only at Level 7, it is hard to catch. Weaken it first, which is why you have a lower level Pokémon with you. And there you have your Mew!

Picture guide:

(Pictures found on Google)