This is the part of my web site on hints for the Pokemon video games:
For Red and Blue:
To catch Mew:
Nintendo may claim that it is only possible to catch Mew by attending
special events, but there is a glitch that can be used. (Note: I got
this info from http://www.angelfire.com/pro/pokeroms).
Do not fight either the Youngster with a Slowpoke on the way to Bill's
house (he's facing north, and directly above a bush or boulder) or the
Gambler with two Poliwags and a Poliwhirl directly below the tunnel
that goes from Celadon City to the Route near Saffron City. After you
have the HM for Fly, go through the tunnel from Celadon to Lavender,
heading toward Lavender. As soon as you come out of the tunnel, save
your game. Then, go one step down and press Start immediately. If the
Gambler sees you and goes up to battle, turn your game off and try
again. When done correctly, your Start Menu will pop up. Select the
Pokemon who knows Fly, and then Fly to Cerulean. The Gambler will see
you, but won't walk up to you. Your Start button won't work now, since
the game thinks you're in a battle. Go up the Nugget Bridge, and battle
the Trainer facing North with the Slowpoke. (Make sure that you don't
walk directly in front of him so he doesn't have to move, or your game
will lock up). After winning, Fly to Lavender (your Start menu will
work fine now) and heal up any injured Pokemon, as well as getting your
Great Balls (or Poke Balls out of the PC). Also get a Pokemon able to
weaken a Level 7 Mew (like a Level 12 Nidoran or something). Then walk
out with your low Pokemon at the front. Attempt to go West to the route
with the Gambler and your Start menu will pop up by itself. Press B,
and a Level 7 Mew will appear. It is possible also to do this trick by
walking in front of the trainer near Nugget Bridge on the left who says
"I saw your feat from the grass!" You can also catch a Magmar by flying
to Vermilion and battling the Engineer who says "Beware of live wires!"
You can also catch Hitmonchan, Nidoqueen, Golem, Gengar, Electabuzz,
Psyduck, and Nidoking using this glitch (all on Level 7).
