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Mew Glitch

Below I have the instructions on how to get Mew.  I have screenshots and instructions.

First of all, do not battle this guy above the Nugget Bridge in Cerulean, , or this guy to the left of Lavender.
Now, go infront of the door that is directly above the man to the left of Lavender. You should save here, in case you mess up. Now, take a step down, and press Start RIGHT BEFORE the trainer see's you. Once you do that, fly to Cerulean. As you fly away, and exclamation point will appear above that trainer, but thats okay. Now go to the trainer in the first picture i showed you. Battle him, but when you do, make him walk to you.
If you dont do make him walk, your game will freeze up, and you'll have to try again. Now beat the trainer, all he has is a lvl 17 slowpoke. After you beat him, fly to Lavendar. Once your in lavendar, , walk to the path on the left. The start menu should pop up.
Now press B or exit out of it, what ever. And mew will appear.
Sure, its only a lvl 7 and all it knows is pound, but it is still pretty hard to capture.
 
 
 
THE EASIER WAY (YOU CAN CATCH MORE THAN 1 MEW THIS WAY)
1. Have a pokemon with a special of 21
2 Fly away from the Gambler battle on route 8(left of lavender)
3. find any trainer and battle him
4.  Fly to anywhere that has a Ditto in the wild
5. Let the wild Ditto transform into your Pokémon with the special of 21
6. Beat the Ditto (or just run away)
DO NOT FACE ANY OTHER POKEMON AFTER THIS!
7. return to route 8 (go to lavender, and walk to the left on that path)
8. if you did the trick correctly, you should be facing another Lvl 7 Mew!
 
You can also use this to get other pokemon.  Do as above, but instead of a pokemon with a special of 21, use a pokemon of the special listed below.
1 - Rhydon
2 - Kangaskhan
3 - NidoranM
4 - Clefairy
( ^ Note: No Pokemon can ever have a natural Special stat below 5.)
5 - Spearow
6 - Voltorb
7 - Nidoking
8 - Slowbro
9 - Ivysaur
10 - Exeggutor
11 - Lickitung
12 - Exeggcute
13 - Grimer
14 - Gengar
15 - NidoranF
16 - Nidoqueen
17 - Cubone
18 - Rhyhorn
19 - Lapras
20 - Arcanine
21 - Mew
22 - Gyarados
23 - Shellder
24 - Tentacool
25 - Gastly
26 - Scyther
27 - Staryu
28 - Blastoise
29 - Pinsir
30 - Tangela
33 - Growlithe
34 - Onix
35 - Fearow
36 - Pidgey
37 - Slowpoke
38 - Kadabra
39 - Graveler
40 - Chansey
41 - Machoke
42 - Mr. Mime
43 - Hitmonlee
44 - Hitmonchan
45 - Arbok
46 - Parasect
47 - Psyduck
48 - Drowzee
49 - Golem
51 - Magmar
52 - Mankey
53 - Electabuzz
54 - Magneton
55 - Koffing
58 - Seel
59 - Diglett
60 - Tauros
64 - Farfetch'd
65 - Venonat
66 - Dragonite
70 - Doduo
71 - Poliwag
72 - Jynx
73 - Moltres
74 - Articuno
75 - Zapdos
76 - Ditto
77 - Meowth
78 - Krabby
82 - Vulpix
83 - Ninetales
84 - Pikachu
85 - Raichu
88 - Dratini
89 - Dragonair
90 - Kabuto
91 - Kabutops
92 - Horsea
93 - Seadra
96 - Sandshrew
97 - Sandslash
98 - Omanyte
99 - Omastar
100 - Jigglypuff
101 - Wigglytuff
102 - Eevee
103 - Flareon
104 - Jolteon
105 - Vaporeon
106 - Machop
107 - Zubat
108 - Ekans
109 - Paras
110 - Poliwhirl
111 - Poliwrath
112 - Weedle
113 - Kakuna
114 - Beedrill
116 - Dodrio
117 - Primeape
118 - Dugtrio
119 - Venomoth
120 - Dewgong
123 - Caterpie
124 - Metapod
125 - Butterfree
126 - Machamp
127 - Missingno.
128 - Golduck
129 - Hypno
130 - Golbat
131 - Mewtwo
132 - Snorlax
133 - Magikarp
136 - Muk
138 - Kingler
139 - Cloyster
141 - Electrode
142 - Clefable
143 - Weezing
144 - Persian
145 - Marowak
147 - Haunter
148 - Abra
149 - Alakazam
150 - Pidgeotto
151 - Pidgeot
152 - Starmie
153 - Bulbasaur
154 - Venusaur
155 - Tentacruel
157 - Goldeen
158 - Seaking
163 - Ponyta
164 - Rapidash
165 - Rattata
166 - Raticate
167 - Nidorino
168 - Nidorina
169 - Geodude
170 - Porygon
171 - Aerodactyl
173 - Magnemite
176 - Charmander
177 - Squirtle
178 - Charmeleon
179 - Wartortle
180 - Charizard
185 - Oddish
186 - Gloom
187 - Vileplume
188 - Bellsprout
189 - Weepinbell
190 - Victreebel
409 = Bulbasaur
437 = Charmander
339 = Ninetails
427 = Aerodactyl
265 = Ivysaur
502 = (Trainer) Agatha (Elite 4) who has: Missingno. Lv. 205 , Seel Lv. 205 , Pikachu Lv. 205 , Seadra Lv. 205 , Growlithe Lv. 205 , L- Yes that was the name it looked sorta like Missingno. but it was a square Lv. 205. BTW, L also duplicates your 5th and 6th item.
505 = Trainer blob(because its name and sprite looked like -m-)
Had 6 pkmn but they were all pixelated and I could not see them. Don't try this one because if you switch pokemn your screen blacks out, and if you beat it it says 9999 999 9999 9999 error 9999 Etc. Doing both of these results in freezing.
414 = Seaking
227 = (Trainer) Cheif w/ Voltorb Lv. 25, Koffing Lv. 25, Magneton Lv. 25, Magnemite Lv. 25, Koffing Lv. 25
430 = Missingno
233 = (trainer) Bruno w/ Growlithe Lv. 42 , Ponyta Lv. 40 , Rapidash Lv. 42 , Arcanine Lv. 47 (Blaine's Pokemon )
257 = Rhydon
259 = NidoranF
209 = (trainer) Hiker w/ Geodude Lv. 21 , Onix Lv. 21
211 = (trainer) Burglar w/ Lv. 34 Charmander , Lv. 34 Charmeleon (in game trainer is in Cinnabar mansion)
221 = (trainer) Juggler w/ Hypno Lv. 38 (in-game location = Koga's Gym)
213 = (trainer) Juggler w/ Seaking Lv. 28, Goldeen Lv. 28, Seaking Lv. 28, Goldeen Lv. 28
214 = (trainer) Fisherman w/ Seaking Lv. 28, Goldeen Lv. 28, Seaking Lv. 28, Goldeen Lv. 28
216 = (trainer) Cue Ball w/ Mankey Lv. 26, Mankey Lv. 26, Machoke Lv. 26, Machop Lv. 26 (in-game location = Cycling road)
217 = (trainer) Gambler w/ Growlithe Lv. 24, Vulpix Lv. 24
219 = (trainer) Psychic w/ Kadabra Lv. 29, Mr. Mime Lv. 29
222 = (trainer) Tamer w/ Pidgey Lv. 24, Pidgeotto Lv. 24 (in-game trainer = Bird keeper east of Fuschia)
269 = Grimer
Thanks to Crystal Mew of Serebii.net
 

Good Luck!!!