Um, just to let you guys know, there IS an easier way to catch mew than starting your game over and flying away from that dude near misty's city. (In Red and Blue)
If you find a pokemon that has a special stat of exactly 21, put it first in your party. (It should be about level 11 or less. My pokemon was a level 12 Butterfree.) I reccomend going to Fuchsia city to do this.
First, Take your pokemon out of the computer. Then, go down the road and head east (to the right). Go down that route, and look in the grass for a ditto. (Make sure all the trainers on that route are beatin and won't challenge you, but make sure you leave a few at the end and you have room to fly away.)
After you battle the ditto and win (with the pokemon with the stats of 21), dont battle anyone or anything else untill you reach the few trainers that you diden't beat. Then, get into a postion where you can fly away when he/she sees you. (I reccomend the bikers near the end of the route).
When you fly away, fly streight back to Fuchsia. Don't battle anything or anyone. Go back to the route and start walking down it, staying out of the grass and trainers that want to battle you. Somewhere on the route, your menue will pop up. YOU MUST PRESS THE B BUTTON AT THIS TIME. When the screen goes down, a level 7 mew will appear. If your smart, you'll have stocked up on masterballs using the MissingNo glitch.
Use masterballs to catch the mew. It should be easy. It'll be hard to train this mew when it gets to higher levels, so when it gets to level 50, I reccomend using rarecandys (obtained by the MissingNo glitch) to train it. Mew will behave like a normal pokemon, not a glitch, after you catch it. I have caught my mew this way, so I know it works.
WARNING!!!! If you use a pokemon with diffrent stats than 21, it'll either come up with a random pokemon, or a glitch. If you encounter a glitch, it could mess up your game perminantly, because some glitches save your game as soon as you encounter them. However, some glitches won't.
BUT, if you do this wrong, it could mess up your game. So, if you want to do this, make sure you do it right.