To get mew through a glitch, you should not have defeated the youngster with the slowbro near bill's house or the gambler between lavender and celadon yet. Also you must have FLY. Make sure you have a weak pokemon below or on lvl 7. Go through the underground passage just outside celadon city. As soon as you exit DON'T MOVE. Save the game then walk one step down and IMMEDIATELY press start - if done correctly the gambler will not see you. In the start menu go to a flying pokemon and fly to cerulean city. The gambler will now have noticed you. In cerulean the start won't work because it thinks you are in battle go over nugget bridge and find the youngster with the slowpoke don't walk directly at him or the game will crash let him walk to you. Defeat him and go to Lavender town. Go to route 8 where the gambler is and the START screen will automatically appear press B and you will find a battle. It will be MEW. Catch him and he is yours.
(Editor's note - this cheat is untested, but you never know...)
Submitted by pokefreak093547