Lol, I still have Blue, and the Mew I had to catch with some obnoxiously difficult exploit, something involving Cerulean City's bridge, that's about all I can remember specifically.
It's the http://bulbapedia.bulbagarden.net/wiki/Mew_glitch
1. Teleport/fly after making a trainer notice you when they first appear on the screen (they must be off-screen, then as soon as they appear on-screen notice you)
2. Battle a pokemon with a special stat of 21 (the slowpoke owned by the Youngster on route 24 is one of the best known examples of this)
3. Walk and eventually the menu will appear, on closing it, you will battle Mew.
http://www.youtube.com/watch?v=dYzFeE6MyX4.
As noted on Bulbapedia, doing this glitch, it's possible to run into a bunch of different pokemon/glitches.