Catching Mew is no longer a hassle. This glitch really does work.
Restart your game and play it until you get HM02 (Fly) from the house west of Celadon City.
* IMPORTANT!: Don't fight the following trainers!: The Youngster who has a Slowpoke, on the road that goes to Bills house. He is the fourth trainer when you get off Nugget Bridge, standing above a female trainer and looking North.
* The Gambler with 2 Poliwags and a Poliwhirl between Lavender Town and Saffron City. He will be standing East of the entrance to Saffron City,looking North near the door of the Underground Path. Carefully follow the steps below.
Make sure you have a pokemon that knows FLY (HM02). Make sure you have a weakish pokemon or a master ball with you. Save your game before you enter Route 8 saving after this point will wreck the procedure.
When your on Route 8, stand in front of the door of the Underground Path (don't let the gambler see you or you will have to restart where you last saved). Walk down one step and Immediately press start. If you get it, the menu will pop up before the Gambler has seen you. Go to your Pokemon and get one that knows, then fly to Cerulean City. The Gambler will see you just before you fly. The Start button wont work like your in the battle. Go across Nugget Bridge and go east until you find the Youngster described above.
If you walk straight up to the Youngster, the game will lock up, you have to make him walk up to you. Beat his Slowpoke(Your start button will work now), then fly to Lavender Town. Head into Route 8. When you get into the narrow path, the menu will come up by itself. Press B to exit and a Mew should appear, Mew will be at Level 7 and it only knows Pound. Once you've caught Mew, you can save without any annoying effects!
NOTE: I did this on my pokemon red game and it should work on the other pokemon red (maybe blue and yellow). It is worth trying it so you can get a Mew just like I did and it is easy to do but it can take a bit of time.
From Nick