well there is a way too catch mew in the original blue and red.Dont know about yellow.
Step 0) Choose a Trainer from my "Trainer One" list that you haven't battled.
Also choose a Trainer (or a Pokemon with the right Special) from the
"Trainer Two" list.
Step 1) Bring a Pokemon with Fly into your party.
Step 2) Get some Ultra Balls, and anything else you would use to
catch a Level 7 Pokemon.
Step 3) Go to the trainer you chose from the "Trainer One" list. Save before the
trainer is on screen. Don't make him/her battle you yet. Now, step one step
towards the trainer, and PRESS START. Really fast. If you did it right,
it will pop up, but the trainer won't battle you. Now Fly to where-ever
the Trainer from "Trainer Two" list is. Or if you have a Pokemon with the right
Special, go anywhere there is a trainer.
Note) If you've done this right, after you use Fly, he will get the "!" over his head.
You cannot use START, A, or B right now.
Note) Do NOT save anywhere after this. First of all, you can't save when
your buttons don't work. But second, when they work again, saving
will negate the glitch, and the important trainer will be defeated,
and not allow you to get the Mew. If you are using a Pokemon with the
Special, and you haven't battled the Ditto yet, you CAN save.
If not, keep your saved file from before you battled Trainer One.
Step 4) Walk (you can't use start) to Trainer Two, and when you battle him,
make sure he WALKS TO YOU. Don't go directly in front of him. Beat him,
and (now your buttons work) Fly to near where Trainer One was.
Step 5) Now, go to the Route where you battled Trainer One. Do NOT save here.
Press B. Mew will appear.
Here is a link to White Cat's site, which gives a complete walkthrough
on how to get Mew, the original way.
http://white-cat.virtualave.net/pfiles/catchmew.htm
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~~~~~~~~~~ 3) Trainer List ~~~~~~~~~~
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The number one rule...
Do NOT talk to other trainers when you're in the middle of this code.
For example, Nurse Joy. If you do, you will battle a trainer twice,
and whenever you go into that where you fought Trainer One, the game will freeze up.
If you did, battle another trainer, or turn the game off/on.
Why? Becuase..get this...PEOPLE do NOT have STATS. Look below, to see
what determines the Pokemon you get. People, do NOT have stats, therefore,
they will not give you pokemon.
Thank you White Cat for this:
"I've figured out what causes Mew to appear.
It's based on the Special stat of the last Pokemon you fought."
It's true. The reason that you always get Mew
from that Slowpoke, is the DVs are fixed.
So, YOU CAN USE WILD POKEMON FOR THIS TRICK!
You must battle a trainer first, then if a wild
one runs into you, you can try it.
And that means...YOU CAN GET UNLIMITED MEWS!
I will find out which Pokemon have a possible
21 (or even 277) special.
If you have battled the Youngster with the Slowpoke,
you can still get a Mew. Go back a couple of lines to the ###.
There are as many Mew in this game as there are trainers. What I'm
saying is, if you SAVE, start the trick, battle a trainer, and battle
a wild pokemon, that may have a Special of 21, you can get a Mew!
If you can find someone with a Special of 131, you may be able to
get a Mewtwo!
If you want to search for something that can be obtained, press
Ctrl + F, for find, and search for "Obtain -) Pokemon".
If something comes up, that will be the trainer you battle.
Now then, special people that you battle, such as forced battles,
Eg: Gary, or button activated battles, Eg: Gym Leaders, and last,
people that don't have space to move when you battle them. They have
to move at least a square. UNLESS, you Activate the code, then
battle someone. You buttons are free, and now you can battle ANOTHER trainer,
giving you only the prize of the last trainer you battled. You can do that with
people like Koga and Blaine.
Now...if I put a * next to something, it means you
must battle another trainer first
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~~~~~~~ 3a) Trainer One List ~~~~~~
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Sorry, too lazy to update this right now.
Gambler, facing the door to the underground path to Celadon.
Super Nerd, right next to him.
Bird Keeper on Route 14, facing up, near a biker.
Look for your own for now :x
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~~~~~~~ 3b) Trainer Two List ~~~~~~
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-------------------
Number -) *#1*
Trainer -) Rival, First Encounter
Location -) Professor Oak's Lab
Pokemon -) B/C/S
Levels -) Level 5
Obtain -) Exeggutor (If he has Bulbasaur, Exeggcute)
I got this from gamefaq and if you read all this you should get mew.If you dont want to read it here go to gamefaqs.com Go to pokemon red faqs and look at the full thing[this isnt the full thing]at the mew glich.this works.